---
_id: '7573'
abstract:
- lang: eng
text: This paper deals with dynamical optimal transport metrics defined by spatial
discretisation of the Benamou–Benamou formula for the Kantorovich metric . Such
metrics appear naturally in discretisations of -gradient flow formulations for
dissipative PDE. However, it has recently been shown that these metrics do not
in general converge to , unless strong geometric constraints are imposed on the
discrete mesh. In this paper we prove that, in a 1-dimensional periodic setting,
discrete transport metrics converge to a limiting transport metric with a non-trivial
effective mobility. This mobility depends sensitively on the geometry of the mesh
and on the non-local mobility at the discrete level. Our result quantifies to
what extent discrete transport can make use of microstructure in the mesh to reduce
the cost of transport.
acknowledgement: J.M. gratefully acknowledges support by the European Research Council
(ERC) under the European Union's Horizon 2020 research and innovation programme
(grant agreement No 716117). J.M. and L.P. also acknowledge support from the Austrian
Science Fund (FWF), grants No F65 and W1245. E.K. gratefully acknowledges support
by the German Research Foundation through the Hausdorff Center for Mathematics and
the Collaborative Research Center 1060. P.G. is partially funded by the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation) – 350398276.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Peter
full_name: Gladbach, Peter
last_name: Gladbach
- first_name: Eva
full_name: Kopfer, Eva
last_name: Kopfer
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Lorenzo
full_name: Portinale, Lorenzo
id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87
last_name: Portinale
citation:
ama: Gladbach P, Kopfer E, Maas J, Portinale L. Homogenisation of one-dimensional
discrete optimal transport. Journal de Mathematiques Pures et Appliquees.
2020;139(7):204-234. doi:10.1016/j.matpur.2020.02.008
apa: Gladbach, P., Kopfer, E., Maas, J., & Portinale, L. (2020). Homogenisation
of one-dimensional discrete optimal transport. Journal de Mathematiques Pures
et Appliquees. Elsevier. https://doi.org/10.1016/j.matpur.2020.02.008
chicago: Gladbach, Peter, Eva Kopfer, Jan Maas, and Lorenzo Portinale. “Homogenisation
of One-Dimensional Discrete Optimal Transport.” Journal de Mathematiques Pures
et Appliquees. Elsevier, 2020. https://doi.org/10.1016/j.matpur.2020.02.008.
ieee: P. Gladbach, E. Kopfer, J. Maas, and L. Portinale, “Homogenisation of one-dimensional
discrete optimal transport,” Journal de Mathematiques Pures et Appliquees,
vol. 139, no. 7. Elsevier, pp. 204–234, 2020.
ista: Gladbach P, Kopfer E, Maas J, Portinale L. 2020. Homogenisation of one-dimensional
discrete optimal transport. Journal de Mathematiques Pures et Appliquees. 139(7),
204–234.
mla: Gladbach, Peter, et al. “Homogenisation of One-Dimensional Discrete Optimal
Transport.” Journal de Mathematiques Pures et Appliquees, vol. 139, no.
7, Elsevier, 2020, pp. 204–34, doi:10.1016/j.matpur.2020.02.008.
short: P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Journal de Mathematiques Pures
et Appliquees 139 (2020) 204–234.
date_created: 2020-03-08T23:00:47Z
date_published: 2020-07-01T00:00:00Z
date_updated: 2023-09-07T13:31:05Z
day: '01'
department:
- _id: JaMa
doi: 10.1016/j.matpur.2020.02.008
ec_funded: 1
external_id:
arxiv:
- '1905.05757'
isi:
- '000539439400008'
intvolume: ' 139'
isi: 1
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1905.05757
month: '07'
oa: 1
oa_version: Preprint
page: 204-234
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: 260482E2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: ' F06504'
name: Taming Complexity in Partial Di erential Systems
- _id: 260788DE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
name: Dissipation and Dispersion in Nonlinear Partial Differential Equations
publication: Journal de Mathematiques Pures et Appliquees
publication_identifier:
issn:
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publication_status: published
publisher: Elsevier
quality_controlled: '1'
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title: Homogenisation of one-dimensional discrete optimal transport
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 139
year: '2020'
...
---
_id: '7629'
abstract:
- lang: eng
text: "This thesis is based on three main topics: In the first part, we study convergence
of discrete gradient flow structures associated with regular finite-volume discretisations
of Fokker-Planck equations. We show evolutionary I convergence of the discrete
gradient flows to the L2-Wasserstein gradient flow corresponding to the solution
of a Fokker-Planck\r\nequation in arbitrary dimension d >= 1. Along the argument,
we prove Mosco- and I-convergence results for discrete energy functionals, which
are of independent interest for convergence of equivalent gradient flow structures
in Hilbert spaces.\r\nThe second part investigates L2-Wasserstein flows on metric
graph. The starting point is a Benamou-Brenier formula for the L2-Wasserstein
distance, which is proved via a regularisation scheme for solutions of the continuity
equation, adapted to the peculiar geometric structure of metric graphs. Based
on those results, we show that the L2-Wasserstein space over a metric graph admits
a gradient flow which may be identified as a solution of a Fokker-Planck equation.\r\nIn
the third part, we focus again on the discrete gradient flows, already encountered
in the first part. We propose a variational structure which extends the gradient
flow structure to Markov chains violating the detailed-balance conditions. Using
this structure, we characterise contraction estimates for the discrete heat flow
in terms of convexity of\r\ncorresponding path-dependent energy functionals. In
addition, we use this approach to derive several functional inequalities for said
functionals."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Dominik L
full_name: Forkert, Dominik L
id: 35C79D68-F248-11E8-B48F-1D18A9856A87
last_name: Forkert
citation:
ama: Forkert DL. Gradient flows in spaces of probability measures for finite-volume
schemes, metric graphs and non-reversible Markov chains. 2020. doi:10.15479/AT:ISTA:7629
apa: Forkert, D. L. (2020). Gradient flows in spaces of probability measures
for finite-volume schemes, metric graphs and non-reversible Markov chains.
Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:7629
chicago: Forkert, Dominik L. “Gradient Flows in Spaces of Probability Measures for
Finite-Volume Schemes, Metric Graphs and Non-Reversible Markov Chains.” Institute
of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7629.
ieee: D. L. Forkert, “Gradient flows in spaces of probability measures for finite-volume
schemes, metric graphs and non-reversible Markov chains,” Institute of Science
and Technology Austria, 2020.
ista: Forkert DL. 2020. Gradient flows in spaces of probability measures for finite-volume
schemes, metric graphs and non-reversible Markov chains. Institute of Science
and Technology Austria.
mla: Forkert, Dominik L. Gradient Flows in Spaces of Probability Measures for
Finite-Volume Schemes, Metric Graphs and Non-Reversible Markov Chains. Institute
of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:7629.
short: D.L. Forkert, Gradient Flows in Spaces of Probability Measures for Finite-Volume
Schemes, Metric Graphs and Non-Reversible Markov Chains, Institute of Science
and Technology Austria, 2020.
date_created: 2020-04-02T06:40:23Z
date_published: 2020-03-31T00:00:00Z
date_updated: 2023-09-07T13:03:12Z
day: '31'
ddc:
- '510'
degree_awarded: PhD
department:
- _id: JaMa
doi: 10.15479/AT:ISTA:7629
ec_funded: 1
file:
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checksum: c814a1a6195269ca6fe48b0dca45ae8a
content_type: application/pdf
creator: dernst
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date_updated: 2020-07-14T12:48:01Z
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language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: '154'
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
status: public
supervisor:
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
title: Gradient flows in spaces of probability measures for finite-volume schemes,
metric graphs and non-reversible Markov chains
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2020'
...
---
_id: '6358'
abstract:
- lang: eng
text: We study dynamical optimal transport metrics between density matricesassociated
to symmetric Dirichlet forms on finite-dimensional C∗-algebras. Our settingcovers arbitrary skew-derivations and it provides a unified framework that simultaneously generalizes recently constructed transport metrics for Markov chains, Lindblad equations, and the Fermi Ornstein–Uhlenbeck semigroup. We develop a non-nommutative
differential calculus that allows us to obtain non-commutative Ricci curvature bounds, logarithmic Sobolev inequalities, transport-entropy inequalities, andspectral
gap estimates.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Eric A.
full_name: Carlen, Eric A.
last_name: Carlen
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
citation:
ama: Carlen EA, Maas J. Non-commutative calculus, optimal transport and functional
inequalities in dissipative quantum systems. Journal of Statistical Physics.
2020;178(2):319-378. doi:10.1007/s10955-019-02434-w
apa: Carlen, E. A., & Maas, J. (2020). Non-commutative calculus, optimal transport
and functional inequalities in dissipative quantum systems. Journal of Statistical
Physics. Springer Nature. https://doi.org/10.1007/s10955-019-02434-w
chicago: Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport
and Functional Inequalities in Dissipative Quantum Systems.” Journal of Statistical
Physics. Springer Nature, 2020. https://doi.org/10.1007/s10955-019-02434-w.
ieee: E. A. Carlen and J. Maas, “Non-commutative calculus, optimal transport and
functional inequalities in dissipative quantum systems,” Journal of Statistical
Physics, vol. 178, no. 2. Springer Nature, pp. 319–378, 2020.
ista: Carlen EA, Maas J. 2020. Non-commutative calculus, optimal transport and functional
inequalities in dissipative quantum systems. Journal of Statistical Physics.
178(2), 319–378.
mla: Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport
and Functional Inequalities in Dissipative Quantum Systems.” Journal of Statistical
Physics, vol. 178, no. 2, Springer Nature, 2020, pp. 319–78, doi:10.1007/s10955-019-02434-w.
short: E.A. Carlen, J. Maas, Journal of Statistical Physics 178 (2020) 319–378.
date_created: 2019-04-30T07:34:18Z
date_published: 2020-01-01T00:00:00Z
date_updated: 2023-08-17T13:49:40Z
day: '01'
ddc:
- '500'
department:
- _id: JaMa
doi: 10.1007/s10955-019-02434-w
ec_funded: 1
external_id:
arxiv:
- '1811.04572'
isi:
- '000498933300001'
file:
- access_level: open_access
checksum: 7b04befbdc0d4982c0ee945d25d19872
content_type: application/pdf
creator: dernst
date_created: 2019-12-23T12:03:09Z
date_updated: 2020-07-14T12:47:28Z
file_id: '7209'
file_name: 2019_JourStatistPhysics_Carlen.pdf
file_size: 905538
relation: main_file
file_date_updated: 2020-07-14T12:47:28Z
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intvolume: ' 178'
isi: 1
issue: '2'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '01'
oa: 1
oa_version: Published Version
page: 319-378
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: 260482E2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: ' F06504'
name: Taming Complexity in Partial Di erential Systems
publication: Journal of Statistical Physics
publication_identifier:
eissn:
- '15729613'
issn:
- '00224715'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
link:
- relation: erratum
url: https://doi.org/10.1007/s10955-020-02671-4
scopus_import: '1'
status: public
title: Non-commutative calculus, optimal transport and functional inequalities in
dissipative quantum systems
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 178
year: '2020'
...
---
_id: '6359'
abstract:
- lang: eng
text: The strong rate of convergence of the Euler-Maruyama scheme for nondegenerate
SDEs with irregular drift coefficients is considered. In the case of α-Hölder
drift in the recent literature the rate α/2 was proved in many related situations.
By exploiting the regularising effect of the noise more efficiently, we show that
the rate is in fact arbitrarily close to 1/2 for all α>0. The result extends to
Dini continuous coefficients, while in d=1 also to all bounded measurable coefficients.
article_number: '82'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Konstantinos
full_name: Dareiotis, Konstantinos
last_name: Dareiotis
- first_name: Mate
full_name: Gerencser, Mate
id: 44ECEDF2-F248-11E8-B48F-1D18A9856A87
last_name: Gerencser
citation:
ama: Dareiotis K, Gerencser M. On the regularisation of the noise for the Euler-Maruyama
scheme with irregular drift. Electronic Journal of Probability. 2020;25.
doi:10.1214/20-EJP479
apa: Dareiotis, K., & Gerencser, M. (2020). On the regularisation of the noise
for the Euler-Maruyama scheme with irregular drift. Electronic Journal of Probability.
Institute of Mathematical Statistics. https://doi.org/10.1214/20-EJP479
chicago: Dareiotis, Konstantinos, and Mate Gerencser. “On the Regularisation of
the Noise for the Euler-Maruyama Scheme with Irregular Drift.” Electronic Journal
of Probability. Institute of Mathematical Statistics, 2020. https://doi.org/10.1214/20-EJP479.
ieee: K. Dareiotis and M. Gerencser, “On the regularisation of the noise for the
Euler-Maruyama scheme with irregular drift,” Electronic Journal of Probability,
vol. 25. Institute of Mathematical Statistics, 2020.
ista: Dareiotis K, Gerencser M. 2020. On the regularisation of the noise for the
Euler-Maruyama scheme with irregular drift. Electronic Journal of Probability.
25, 82.
mla: Dareiotis, Konstantinos, and Mate Gerencser. “On the Regularisation of the
Noise for the Euler-Maruyama Scheme with Irregular Drift.” Electronic Journal
of Probability, vol. 25, 82, Institute of Mathematical Statistics, 2020, doi:10.1214/20-EJP479.
short: K. Dareiotis, M. Gerencser, Electronic Journal of Probability 25 (2020).
date_created: 2019-04-30T07:40:17Z
date_published: 2020-07-16T00:00:00Z
date_updated: 2023-10-16T09:22:50Z
day: '16'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1214/20-EJP479
external_id:
arxiv:
- '1812.04583'
isi:
- '000550150700001'
file:
- access_level: open_access
checksum: 8e7c42e72596f6889d786e8e8b89994f
content_type: application/pdf
creator: dernst
date_created: 2020-09-21T13:15:02Z
date_updated: 2020-09-21T13:15:02Z
file_id: '8549'
file_name: 2020_EJournProbab_Dareiotis.pdf
file_size: 273042
relation: main_file
success: 1
file_date_updated: 2020-09-21T13:15:02Z
has_accepted_license: '1'
intvolume: ' 25'
isi: 1
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
publication: Electronic Journal of Probability
publication_identifier:
eissn:
- 1083-6489
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the regularisation of the noise for the Euler-Maruyama scheme with irregular
drift
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 25
year: '2020'
...
---
_id: '10022'
abstract:
- lang: eng
text: We consider finite-volume approximations of Fokker-Planck equations on bounded
convex domains in R^d and study the corresponding gradient flow structures. We
reprove the convergence of the discrete to continuous Fokker-Planck equation via
the method of Evolutionary Γ-convergence, i.e., we pass to the limit at the level
of the gradient flow structures, generalising the one-dimensional result obtained
by Disser and Liero. The proof is of variational nature and relies on a Mosco
convergence result for functionals in the discrete-to-continuum limit that is
of independent interest. Our results apply to arbitrary regular meshes, even though
the associated discrete transport distances may fail to converge to the Wasserstein
distance in this generality.
acknowledgement: This work is supported by the European Research Council (ERC) under
the European Union’s Horizon 2020 research and innovation programme (grant agreement
No 716117) and by the Austrian Science Fund (FWF), grants No F65 and W1245.
article_number: '2008.10962'
article_processing_charge: No
arxiv: 1
author:
- first_name: Dominik L
full_name: Forkert, Dominik L
id: 35C79D68-F248-11E8-B48F-1D18A9856A87
last_name: Forkert
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Lorenzo
full_name: Portinale, Lorenzo
id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87
last_name: Portinale
citation:
ama: Forkert DL, Maas J, Portinale L. Evolutionary Γ-convergence of entropic gradient
flow structures for Fokker-Planck equations in multiple dimensions. arXiv.
apa: Forkert, D. L., Maas, J., & Portinale, L. (n.d.). Evolutionary Γ-convergence
of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions.
arXiv.
chicago: Forkert, Dominik L, Jan Maas, and Lorenzo Portinale. “Evolutionary Γ-Convergence
of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.”
ArXiv, n.d.
ieee: D. L. Forkert, J. Maas, and L. Portinale, “Evolutionary Γ-convergence of entropic
gradient flow structures for Fokker-Planck equations in multiple dimensions,”
arXiv. .
ista: Forkert DL, Maas J, Portinale L. Evolutionary Γ-convergence of entropic gradient
flow structures for Fokker-Planck equations in multiple dimensions. arXiv, 2008.10962.
mla: Forkert, Dominik L., et al. “Evolutionary Γ-Convergence of Entropic Gradient
Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” ArXiv,
2008.10962.
short: D.L. Forkert, J. Maas, L. Portinale, ArXiv (n.d.).
date_created: 2021-09-17T10:57:27Z
date_published: 2020-08-25T00:00:00Z
date_updated: 2023-09-07T13:31:05Z
day: '25'
department:
- _id: JaMa
ec_funded: 1
external_id:
arxiv:
- '2008.10962'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2008.10962
month: '08'
oa: 1
oa_version: Preprint
page: '33'
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: arXiv
publication_status: submitted
related_material:
record:
- id: '11739'
relation: later_version
status: public
- id: '10030'
relation: dissertation_contains
status: public
status: public
title: Evolutionary Γ-convergence of entropic gradient flow structures for Fokker-Planck
equations in multiple dimensions
type: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2020'
...
---
_id: '301'
abstract:
- lang: eng
text: A representation formula for solutions of stochastic partial differential
equations with Dirichlet boundary conditions is proved. The scope of our setting
is wide enough to cover the general situation when the backward characteristics
that appear in the usual formulation are not even defined in the Itô sense.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Mate
full_name: Gerencser, Mate
id: 44ECEDF2-F248-11E8-B48F-1D18A9856A87
last_name: Gerencser
- first_name: István
full_name: Gyöngy, István
last_name: Gyöngy
citation:
ama: Gerencser M, Gyöngy I. A Feynman–Kac formula for stochastic Dirichlet problems.
Stochastic Processes and their Applications. 2019;129(3):995-1012. doi:10.1016/j.spa.2018.04.003
apa: Gerencser, M., & Gyöngy, I. (2019). A Feynman–Kac formula for stochastic
Dirichlet problems. Stochastic Processes and Their Applications. Elsevier.
https://doi.org/10.1016/j.spa.2018.04.003
chicago: Gerencser, Mate, and István Gyöngy. “A Feynman–Kac Formula for Stochastic
Dirichlet Problems.” Stochastic Processes and Their Applications. Elsevier,
2019. https://doi.org/10.1016/j.spa.2018.04.003.
ieee: M. Gerencser and I. Gyöngy, “A Feynman–Kac formula for stochastic Dirichlet
problems,” Stochastic Processes and their Applications, vol. 129, no. 3.
Elsevier, pp. 995–1012, 2019.
ista: Gerencser M, Gyöngy I. 2019. A Feynman–Kac formula for stochastic Dirichlet
problems. Stochastic Processes and their Applications. 129(3), 995–1012.
mla: Gerencser, Mate, and István Gyöngy. “A Feynman–Kac Formula for Stochastic Dirichlet
Problems.” Stochastic Processes and Their Applications, vol. 129, no. 3,
Elsevier, 2019, pp. 995–1012, doi:10.1016/j.spa.2018.04.003.
short: M. Gerencser, I. Gyöngy, Stochastic Processes and Their Applications 129
(2019) 995–1012.
date_created: 2018-12-11T11:45:42Z
date_published: 2019-03-01T00:00:00Z
date_updated: 2023-08-24T14:20:49Z
day: '01'
department:
- _id: JaMa
doi: 10.1016/j.spa.2018.04.003
external_id:
arxiv:
- '1611.04177'
isi:
- '000458945300012'
intvolume: ' 129'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1611.04177
month: '03'
oa: 1
oa_version: Preprint
page: 995-1012
publication: Stochastic Processes and their Applications
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: A Feynman–Kac formula for stochastic Dirichlet problems
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 129
year: '2019'
...
---
_id: '319'
abstract:
- lang: eng
text: We study spaces of modelled distributions with singular behaviour near the
boundary of a domain that, in the context of the theory of regularity structures,
allow one to give robust solution theories for singular stochastic PDEs with boundary
conditions. The calculus of modelled distributions established in Hairer (Invent
Math 198(2):269–504, 2014. https://doi.org/10.1007/s00222-014-0505-4) is extended
to this setting. We formulate and solve fixed point problems in these spaces with
a class of kernels that is sufficiently large to cover in particular the Dirichlet
and Neumann heat kernels. These results are then used to provide solution theories
for the KPZ equation with Dirichlet and Neumann boundary conditions and for the
2D generalised parabolic Anderson model with Dirichlet boundary conditions. In
the case of the KPZ equation with Neumann boundary conditions, we show that, depending
on the class of mollifiers one considers, a “boundary renormalisation” takes place.
In other words, there are situations in which a certain boundary condition is
applied to an approximation to the KPZ equation, but the limiting process is the
Hopf–Cole solution to the KPZ equation with a different boundary condition.
acknowledgement: "MG thanks the support of the LMS Postdoctoral Mobility Grant.\r\n\r\n"
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Mate
full_name: Gerencser, Mate
id: 44ECEDF2-F248-11E8-B48F-1D18A9856A87
last_name: Gerencser
- first_name: Martin
full_name: Hairer, Martin
last_name: Hairer
citation:
ama: Gerencser M, Hairer M. Singular SPDEs in domains with boundaries. Probability
Theory and Related Fields. 2019;173(3-4):697–758. doi:10.1007/s00440-018-0841-1
apa: Gerencser, M., & Hairer, M. (2019). Singular SPDEs in domains with boundaries.
Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-018-0841-1
chicago: Gerencser, Mate, and Martin Hairer. “Singular SPDEs in Domains with Boundaries.”
Probability Theory and Related Fields. Springer, 2019. https://doi.org/10.1007/s00440-018-0841-1.
ieee: M. Gerencser and M. Hairer, “Singular SPDEs in domains with boundaries,” Probability
Theory and Related Fields, vol. 173, no. 3–4. Springer, pp. 697–758, 2019.
ista: Gerencser M, Hairer M. 2019. Singular SPDEs in domains with boundaries. Probability
Theory and Related Fields. 173(3–4), 697–758.
mla: Gerencser, Mate, and Martin Hairer. “Singular SPDEs in Domains with Boundaries.”
Probability Theory and Related Fields, vol. 173, no. 3–4, Springer, 2019,
pp. 697–758, doi:10.1007/s00440-018-0841-1.
short: M. Gerencser, M. Hairer, Probability Theory and Related Fields 173 (2019)
697–758.
date_created: 2018-12-11T11:45:48Z
date_published: 2019-04-01T00:00:00Z
date_updated: 2023-08-24T14:38:32Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00440-018-0841-1
external_id:
isi:
- '000463613800001'
file:
- access_level: open_access
checksum: 288d16ef7291242f485a9660979486e3
content_type: application/pdf
creator: dernst
date_created: 2018-12-17T16:25:24Z
date_updated: 2020-07-14T12:46:03Z
file_id: '5722'
file_name: 2018_ProbTheory_Gerencser.pdf
file_size: 893182
relation: main_file
file_date_updated: 2020-07-14T12:46:03Z
has_accepted_license: '1'
intvolume: ' 173'
isi: 1
issue: 3-4
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 697–758
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Probability Theory and Related Fields
publication_identifier:
eissn:
- '14322064'
issn:
- '01788051'
publication_status: published
publisher: Springer
publist_id: '7546'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Singular SPDEs in domains with boundaries
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 173
year: '2019'
...
---
_id: '10878'
abstract:
- lang: eng
text: Starting from a microscopic model for a system of neurons evolving in time
which individually follow a stochastic integrate-and-fire type model, we study
a mean-field limit of the system. Our model is described by a system of SDEs with
discontinuous coefficients for the action potential of each neuron and takes into
account the (random) spatial configuration of neurons allowing the interaction
to depend on it. In the limit as the number of particles tends to infinity, we
obtain a nonlinear Fokker-Planck type PDE in two variables, with derivatives only
with respect to one variable and discontinuous coefficients. We also study strong
well-posedness of the system of SDEs and prove the existence and uniqueness of
a weak measure-valued solution to the PDE, obtained as the limit of the laws of
the empirical measures for the system of particles.
acknowledgement: "The second author has been partially supported by INdAM through
the GNAMPA Research\r\nProject (2017) “Sistemi stocastici singolari: buona posizione
e problemi di controllo”. The third\r\nauthor was partly funded by the Austrian
Science Fund (FWF) project F 65."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Franco
full_name: Flandoli, Franco
last_name: Flandoli
- first_name: Enrico
full_name: Priola, Enrico
last_name: Priola
- first_name: Giovanni A
full_name: Zanco, Giovanni A
id: 47491882-F248-11E8-B48F-1D18A9856A87
last_name: Zanco
citation:
ama: Flandoli F, Priola E, Zanco GA. A mean-field model with discontinuous coefficients
for neurons with spatial interaction. Discrete and Continuous Dynamical Systems.
2019;39(6):3037-3067. doi:10.3934/dcds.2019126
apa: Flandoli, F., Priola, E., & Zanco, G. A. (2019). A mean-field model with
discontinuous coefficients for neurons with spatial interaction. Discrete and
Continuous Dynamical Systems. American Institute of Mathematical Sciences.
https://doi.org/10.3934/dcds.2019126
chicago: Flandoli, Franco, Enrico Priola, and Giovanni A Zanco. “A Mean-Field Model
with Discontinuous Coefficients for Neurons with Spatial Interaction.” Discrete
and Continuous Dynamical Systems. American Institute of Mathematical Sciences,
2019. https://doi.org/10.3934/dcds.2019126.
ieee: F. Flandoli, E. Priola, and G. A. Zanco, “A mean-field model with discontinuous
coefficients for neurons with spatial interaction,” Discrete and Continuous
Dynamical Systems, vol. 39, no. 6. American Institute of Mathematical Sciences,
pp. 3037–3067, 2019.
ista: Flandoli F, Priola E, Zanco GA. 2019. A mean-field model with discontinuous
coefficients for neurons with spatial interaction. Discrete and Continuous Dynamical
Systems. 39(6), 3037–3067.
mla: Flandoli, Franco, et al. “A Mean-Field Model with Discontinuous Coefficients
for Neurons with Spatial Interaction.” Discrete and Continuous Dynamical Systems,
vol. 39, no. 6, American Institute of Mathematical Sciences, 2019, pp. 3037–67,
doi:10.3934/dcds.2019126.
short: F. Flandoli, E. Priola, G.A. Zanco, Discrete and Continuous Dynamical Systems
39 (2019) 3037–3067.
date_created: 2022-03-18T12:33:34Z
date_published: 2019-06-01T00:00:00Z
date_updated: 2023-09-08T11:34:45Z
day: '01'
department:
- _id: JaMa
doi: 10.3934/dcds.2019126
external_id:
arxiv:
- '1708.04156'
isi:
- '000459954800003'
intvolume: ' 39'
isi: 1
issue: '6'
keyword:
- Applied Mathematics
- Discrete Mathematics and Combinatorics
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1708.04156
month: '06'
oa: 1
oa_version: Preprint
page: 3037-3067
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Discrete and Continuous Dynamical Systems
publication_identifier:
issn:
- 1553-5231
publication_status: published
publisher: American Institute of Mathematical Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: A mean-field model with discontinuous coefficients for neurons with spatial
interaction
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 39
year: '2019'
...
---
_id: '72'
abstract:
- lang: eng
text: We consider the totally asymmetric simple exclusion process (TASEP) with non-random
initial condition having density ρ on ℤ− and λ on ℤ+, and a second class particle
initially at the origin. For ρ<λ, there is a shock and the second class particle
moves with speed 1−λ−ρ. For large time t, we show that the position of the second
class particle fluctuates on a t1/3 scale and determine its limiting law. We also
obtain the limiting distribution of the number of steps made by the second class
particle until time t.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Patrick
full_name: Ferrari, Patrick
last_name: Ferrari
- first_name: Promit
full_name: Ghosal, Promit
last_name: Ghosal
- first_name: Peter
full_name: Nejjar, Peter
id: 4BF426E2-F248-11E8-B48F-1D18A9856A87
last_name: Nejjar
citation:
ama: Ferrari P, Ghosal P, Nejjar P. Limit law of a second class particle in TASEP
with non-random initial condition. Annales de l’institut Henri Poincare (B)
Probability and Statistics. 2019;55(3):1203-1225. doi:10.1214/18-AIHP916
apa: Ferrari, P., Ghosal, P., & Nejjar, P. (2019). Limit law of a second class
particle in TASEP with non-random initial condition. Annales de l’institut
Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics.
https://doi.org/10.1214/18-AIHP916
chicago: Ferrari, Patrick, Promit Ghosal, and Peter Nejjar. “Limit Law of a Second
Class Particle in TASEP with Non-Random Initial Condition.” Annales de l’institut
Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics,
2019. https://doi.org/10.1214/18-AIHP916.
ieee: P. Ferrari, P. Ghosal, and P. Nejjar, “Limit law of a second class particle
in TASEP with non-random initial condition,” Annales de l’institut Henri Poincare
(B) Probability and Statistics, vol. 55, no. 3. Institute of Mathematical
Statistics, pp. 1203–1225, 2019.
ista: Ferrari P, Ghosal P, Nejjar P. 2019. Limit law of a second class particle
in TASEP with non-random initial condition. Annales de l’institut Henri Poincare
(B) Probability and Statistics. 55(3), 1203–1225.
mla: Ferrari, Patrick, et al. “Limit Law of a Second Class Particle in TASEP with
Non-Random Initial Condition.” Annales de l’institut Henri Poincare (B) Probability
and Statistics, vol. 55, no. 3, Institute of Mathematical Statistics, 2019,
pp. 1203–25, doi:10.1214/18-AIHP916.
short: P. Ferrari, P. Ghosal, P. Nejjar, Annales de l’institut Henri Poincare (B)
Probability and Statistics 55 (2019) 1203–1225.
date_created: 2018-12-11T11:44:29Z
date_published: 2019-09-25T00:00:00Z
date_updated: 2023-10-17T08:53:45Z
day: '25'
department:
- _id: LaEr
- _id: JaMa
doi: 10.1214/18-AIHP916
ec_funded: 1
external_id:
arxiv:
- '1710.02323'
isi:
- '000487763200001'
intvolume: ' 55'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1710.02323
month: '09'
oa: 1
oa_version: Preprint
page: 1203-1225
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Annales de l'institut Henri Poincare (B) Probability and Statistics
publication_identifier:
issn:
- 0246-0203
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Limit law of a second class particle in TASEP with non-random initial condition
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 55
year: '2019'
...
---
_id: '73'
abstract:
- lang: eng
text: We consider the space of probability measures on a discrete set X, endowed
with a dynamical optimal transport metric. Given two probability measures supported
in a subset Y⊆X, it is natural to ask whether they can be connected by a constant
speed geodesic with support in Y at all times. Our main result answers this question
affirmatively, under a suitable geometric condition on Y introduced in this paper.
The proof relies on an extension result for subsolutions to discrete Hamilton-Jacobi
equations, which is of independent interest.
article_number: '19'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Matthias
full_name: Erbar, Matthias
last_name: Erbar
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Melchior
full_name: Wirth, Melchior
last_name: Wirth
citation:
ama: Erbar M, Maas J, Wirth M. On the geometry of geodesics in discrete optimal
transport. Calculus of Variations and Partial Differential Equations. 2019;58(1).
doi:10.1007/s00526-018-1456-1
apa: Erbar, M., Maas, J., & Wirth, M. (2019). On the geometry of geodesics in
discrete optimal transport. Calculus of Variations and Partial Differential
Equations. Springer. https://doi.org/10.1007/s00526-018-1456-1
chicago: Erbar, Matthias, Jan Maas, and Melchior Wirth. “On the Geometry of Geodesics
in Discrete Optimal Transport.” Calculus of Variations and Partial Differential
Equations. Springer, 2019. https://doi.org/10.1007/s00526-018-1456-1.
ieee: M. Erbar, J. Maas, and M. Wirth, “On the geometry of geodesics in discrete
optimal transport,” Calculus of Variations and Partial Differential Equations,
vol. 58, no. 1. Springer, 2019.
ista: Erbar M, Maas J, Wirth M. 2019. On the geometry of geodesics in discrete optimal
transport. Calculus of Variations and Partial Differential Equations. 58(1), 19.
mla: Erbar, Matthias, et al. “On the Geometry of Geodesics in Discrete Optimal Transport.”
Calculus of Variations and Partial Differential Equations, vol. 58, no.
1, 19, Springer, 2019, doi:10.1007/s00526-018-1456-1.
short: M. Erbar, J. Maas, M. Wirth, Calculus of Variations and Partial Differential
Equations 58 (2019).
date_created: 2018-12-11T11:44:29Z
date_published: 2019-02-01T00:00:00Z
date_updated: 2023-09-13T09:12:35Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00526-018-1456-1
ec_funded: 1
external_id:
arxiv:
- '1805.06040'
isi:
- '000452849400001'
file:
- access_level: open_access
checksum: ba05ac2d69de4c58d2cd338b63512798
content_type: application/pdf
creator: dernst
date_created: 2019-01-28T15:37:11Z
date_updated: 2020-07-14T12:47:55Z
file_id: '5895'
file_name: 2018_Calculus_Erbar.pdf
file_size: 645565
relation: main_file
file_date_updated: 2020-07-14T12:47:55Z
has_accepted_license: '1'
intvolume: ' 58'
isi: 1
issue: '1'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: 260482E2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: ' F06504'
name: Taming Complexity in Partial Di erential Systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Calculus of Variations and Partial Differential Equations
publication_identifier:
issn:
- '09442669'
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the geometry of geodesics in discrete optimal transport
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 58
year: '2019'
...
---
_id: '7550'
abstract:
- lang: eng
text: 'We consider an optimal control problem for an abstract nonlinear dissipative
evolution equation. The differential constraint is penalized by augmenting the
target functional by a nonnegative global-in-time functional which is null-minimized
in the evolution equation is satisfied. Different variational settings are presented,
leading to the convergence of the penalization method for gradient flows, noncyclic
and semimonotone flows, doubly nonlinear evolutions, and GENERIC systems. '
acknowledgement: This work is supported by Vienna Science and Technology Fund (WWTF)
through Project MA14-009 and by the Austrian Science Fund (FWF) projects F 65 and
I 2375.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Portinale, Lorenzo
id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87
last_name: Portinale
- first_name: Ulisse
full_name: Stefanelli, Ulisse
last_name: Stefanelli
citation:
ama: Portinale L, Stefanelli U. Penalization via global functionals of optimal-control
problems for dissipative evolution. Advances in Mathematical Sciences and Applications.
2019;28(2):425-447.
apa: Portinale, L., & Stefanelli, U. (2019). Penalization via global functionals
of optimal-control problems for dissipative evolution. Advances in Mathematical
Sciences and Applications. Gakko Tosho.
chicago: Portinale, Lorenzo, and Ulisse Stefanelli. “Penalization via Global Functionals
of Optimal-Control Problems for Dissipative Evolution.” Advances in Mathematical
Sciences and Applications. Gakko Tosho, 2019.
ieee: L. Portinale and U. Stefanelli, “Penalization via global functionals of optimal-control
problems for dissipative evolution,” Advances in Mathematical Sciences and
Applications, vol. 28, no. 2. Gakko Tosho, pp. 425–447, 2019.
ista: Portinale L, Stefanelli U. 2019. Penalization via global functionals of optimal-control
problems for dissipative evolution. Advances in Mathematical Sciences and Applications.
28(2), 425–447.
mla: Portinale, Lorenzo, and Ulisse Stefanelli. “Penalization via Global Functionals
of Optimal-Control Problems for Dissipative Evolution.” Advances in Mathematical
Sciences and Applications, vol. 28, no. 2, Gakko Tosho, 2019, pp. 425–47.
short: L. Portinale, U. Stefanelli, Advances in Mathematical Sciences and Applications
28 (2019) 425–447.
date_created: 2020-02-28T10:54:41Z
date_published: 2019-10-22T00:00:00Z
date_updated: 2022-06-17T07:52:41Z
day: '22'
department:
- _id: JaMa
external_id:
arxiv:
- '1910.10050'
intvolume: ' 28'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.1910.10050'
month: '10'
oa: 1
oa_version: Preprint
page: 425-447
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Advances in Mathematical Sciences and Applications
publication_identifier:
issn:
- 1343-4373
publication_status: published
publisher: Gakko Tosho
quality_controlled: '1'
status: public
title: Penalization via global functionals of optimal-control problems for dissipative
evolution
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2019'
...
---
_id: '6028'
abstract:
- lang: eng
text: We give a construction allowing us to build local renormalized solutions to
general quasilinear stochastic PDEs within the theory of regularity structures,
thus greatly generalizing the recent results of [1, 5, 11]. Loosely speaking,
our construction covers quasilinear variants of all classes of equations for which
the general construction of [3, 4, 7] applies, including in particular one‐dimensional
systems with KPZ‐type nonlinearities driven by space‐time white noise. In a less
singular and more specific case, we furthermore show that the counterterms introduced
by the renormalization procedure are given by local functionals of the solution.
The main feature of our construction is that it allows exploitation of a number
of existing results developed for the semilinear case, so that the number of additional
arguments it requires is relatively small.
article_processing_charge: Yes (via OA deal)
author:
- first_name: Mate
full_name: Gerencser, Mate
id: 44ECEDF2-F248-11E8-B48F-1D18A9856A87
last_name: Gerencser
- first_name: Martin
full_name: Hairer, Martin
last_name: Hairer
citation:
ama: Gerencser M, Hairer M. A solution theory for quasilinear singular SPDEs. Communications
on Pure and Applied Mathematics. 2019;72(9):1983-2005. doi:10.1002/cpa.21816
apa: Gerencser, M., & Hairer, M. (2019). A solution theory for quasilinear singular
SPDEs. Communications on Pure and Applied Mathematics. Wiley. https://doi.org/10.1002/cpa.21816
chicago: Gerencser, Mate, and Martin Hairer. “A Solution Theory for Quasilinear
Singular SPDEs.” Communications on Pure and Applied Mathematics. Wiley,
2019. https://doi.org/10.1002/cpa.21816.
ieee: M. Gerencser and M. Hairer, “A solution theory for quasilinear singular SPDEs,”
Communications on Pure and Applied Mathematics, vol. 72, no. 9. Wiley,
pp. 1983–2005, 2019.
ista: Gerencser M, Hairer M. 2019. A solution theory for quasilinear singular SPDEs.
Communications on Pure and Applied Mathematics. 72(9), 1983–2005.
mla: Gerencser, Mate, and Martin Hairer. “A Solution Theory for Quasilinear Singular
SPDEs.” Communications on Pure and Applied Mathematics, vol. 72, no. 9,
Wiley, 2019, pp. 1983–2005, doi:10.1002/cpa.21816.
short: M. Gerencser, M. Hairer, Communications on Pure and Applied Mathematics 72
(2019) 1983–2005.
date_created: 2019-02-17T22:59:24Z
date_published: 2019-02-08T00:00:00Z
date_updated: 2023-08-24T14:44:31Z
day: '08'
ddc:
- '500'
department:
- _id: JaMa
doi: 10.1002/cpa.21816
external_id:
isi:
- '000475465000003'
file:
- access_level: open_access
checksum: 09aec427eb48c0f96a1cce9ff53f013b
content_type: application/pdf
creator: kschuh
date_created: 2020-01-07T13:25:55Z
date_updated: 2020-07-14T12:47:17Z
file_id: '7237'
file_name: 2019_Wiley_Gerencser.pdf
file_size: 381350
relation: main_file
file_date_updated: 2020-07-14T12:47:17Z
has_accepted_license: '1'
intvolume: ' 72'
isi: 1
issue: '9'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 1983-2005
publication: Communications on Pure and Applied Mathematics
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: A solution theory for quasilinear singular SPDEs
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 72
year: '2019'
...
---
_id: '6232'
abstract:
- lang: eng
text: 'The boundary behaviour of solutions of stochastic PDEs with Dirichlet boundary
conditions can be surprisingly—and in a sense, arbitrarily—bad: as shown by Krylov[
SIAM J. Math. Anal.34(2003) 1167–1182], for any α>0 one can find a simple 1-dimensional
constant coefficient linear equation whose solution at the boundary is not α-Hölder
continuous.We obtain a positive counterpart of this: under some mild regularity
assumptions on the coefficients, solutions of semilinear SPDEs on C1 domains are
proved to be α-Hölder continuous up to the boundary with some α>0.'
article_processing_charge: No
arxiv: 1
author:
- first_name: Mate
full_name: Gerencser, Mate
id: 44ECEDF2-F248-11E8-B48F-1D18A9856A87
last_name: Gerencser
citation:
ama: Gerencser M. Boundary regularity of stochastic PDEs. Annals of Probability.
2019;47(2):804-834. doi:10.1214/18-AOP1272
apa: Gerencser, M. (2019). Boundary regularity of stochastic PDEs. Annals of
Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/18-AOP1272
chicago: Gerencser, Mate. “Boundary Regularity of Stochastic PDEs.” Annals of
Probability. Institute of Mathematical Statistics, 2019. https://doi.org/10.1214/18-AOP1272.
ieee: M. Gerencser, “Boundary regularity of stochastic PDEs,” Annals of Probability,
vol. 47, no. 2. Institute of Mathematical Statistics, pp. 804–834, 2019.
ista: Gerencser M. 2019. Boundary regularity of stochastic PDEs. Annals of Probability.
47(2), 804–834.
mla: Gerencser, Mate. “Boundary Regularity of Stochastic PDEs.” Annals of Probability,
vol. 47, no. 2, Institute of Mathematical Statistics, 2019, pp. 804–34, doi:10.1214/18-AOP1272.
short: M. Gerencser, Annals of Probability 47 (2019) 804–834.
date_created: 2019-04-07T21:59:15Z
date_published: 2019-03-01T00:00:00Z
date_updated: 2023-08-25T08:59:11Z
day: '01'
department:
- _id: JaMa
doi: 10.1214/18-AOP1272
external_id:
arxiv:
- '1705.05364'
isi:
- '000459681900005'
intvolume: ' 47'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1705.05364
month: '03'
oa: 1
oa_version: Preprint
page: 804-834
publication: Annals of Probability
publication_identifier:
issn:
- '00911798'
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Boundary regularity of stochastic PDEs
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 47
year: '2019'
...
---
_id: '65'
abstract:
- lang: eng
text: We provide an entropy formulation for porous medium-type equations with a
stochastic, non-linear, spatially inhomogeneous forcing. Well-posedness and L1-contraction
is obtained in the class of entropy solutions. Our scope allows for porous medium
operators Δ(|u|m−1u) for all m∈(1,∞), and Hölder continuous diffusion nonlinearity
with exponent 1/2.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Konstantinos
full_name: Dareiotis, Konstantinos
last_name: Dareiotis
- first_name: Mate
full_name: Gerencser, Mate
id: 44ECEDF2-F248-11E8-B48F-1D18A9856A87
last_name: Gerencser
- first_name: Benjamin
full_name: Gess, Benjamin
last_name: Gess
citation:
ama: Dareiotis K, Gerencser M, Gess B. Entropy solutions for stochastic porous media
equations. Journal of Differential Equations. 2019;266(6):3732-3763. doi:10.1016/j.jde.2018.09.012
apa: Dareiotis, K., Gerencser, M., & Gess, B. (2019). Entropy solutions for
stochastic porous media equations. Journal of Differential Equations. Elsevier.
https://doi.org/10.1016/j.jde.2018.09.012
chicago: Dareiotis, Konstantinos, Mate Gerencser, and Benjamin Gess. “Entropy Solutions
for Stochastic Porous Media Equations.” Journal of Differential Equations.
Elsevier, 2019. https://doi.org/10.1016/j.jde.2018.09.012.
ieee: K. Dareiotis, M. Gerencser, and B. Gess, “Entropy solutions for stochastic
porous media equations,” Journal of Differential Equations, vol. 266, no.
6. Elsevier, pp. 3732–3763, 2019.
ista: Dareiotis K, Gerencser M, Gess B. 2019. Entropy solutions for stochastic porous
media equations. Journal of Differential Equations. 266(6), 3732–3763.
mla: Dareiotis, Konstantinos, et al. “Entropy Solutions for Stochastic Porous Media
Equations.” Journal of Differential Equations, vol. 266, no. 6, Elsevier,
2019, pp. 3732–63, doi:10.1016/j.jde.2018.09.012.
short: K. Dareiotis, M. Gerencser, B. Gess, Journal of Differential Equations 266
(2019) 3732–3763.
date_created: 2018-12-11T11:44:26Z
date_published: 2019-03-05T00:00:00Z
date_updated: 2023-08-24T14:30:16Z
day: '5'
department:
- _id: JaMa
doi: 10.1016/j.jde.2018.09.012
external_id:
arxiv:
- '1803.06953'
isi:
- '000456332500026'
intvolume: ' 266'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1803.06953
month: '03'
oa: 1
oa_version: Preprint
page: 3732-3763
publication: Journal of Differential Equations
publication_status: published
publisher: Elsevier
publist_id: '7989'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Entropy solutions for stochastic porous media equations
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 266
year: '2019'
...
---
_id: '70'
abstract:
- lang: eng
text: We consider the totally asymmetric simple exclusion process in a critical
scaling parametrized by a≥0, which creates a shock in the particle density of
order aT−1/3, T the observation time. When starting from step initial data, we
provide bounds on the limiting law which in particular imply that in the double
limit lima→∞limT→∞ one recovers the product limit law and the degeneration of
the correlation length observed at shocks of order 1. This result is shown to
apply to a general last-passage percolation model. We also obtain bounds on the
two-point functions of several airy processes.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Peter
full_name: Nejjar, Peter
id: 4BF426E2-F248-11E8-B48F-1D18A9856A87
last_name: Nejjar
citation:
ama: Nejjar P. Transition to shocks in TASEP and decoupling of last passage times.
Latin American Journal of Probability and Mathematical Statistics. 2018;15(2):1311-1334.
doi:10.30757/ALEA.v15-49
apa: Nejjar, P. (2018). Transition to shocks in TASEP and decoupling of last passage
times. Latin American Journal of Probability and Mathematical Statistics.
Instituto Nacional de Matematica Pura e Aplicada. https://doi.org/10.30757/ALEA.v15-49
chicago: Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage
Times.” Latin American Journal of Probability and Mathematical Statistics.
Instituto Nacional de Matematica Pura e Aplicada, 2018. https://doi.org/10.30757/ALEA.v15-49.
ieee: P. Nejjar, “Transition to shocks in TASEP and decoupling of last passage times,”
Latin American Journal of Probability and Mathematical Statistics, vol.
15, no. 2. Instituto Nacional de Matematica Pura e Aplicada, pp. 1311–1334, 2018.
ista: Nejjar P. 2018. Transition to shocks in TASEP and decoupling of last passage
times. Latin American Journal of Probability and Mathematical Statistics. 15(2),
1311–1334.
mla: Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage
Times.” Latin American Journal of Probability and Mathematical Statistics,
vol. 15, no. 2, Instituto Nacional de Matematica Pura e Aplicada, 2018, pp. 1311–34,
doi:10.30757/ALEA.v15-49.
short: P. Nejjar, Latin American Journal of Probability and Mathematical Statistics
15 (2018) 1311–1334.
date_created: 2018-12-11T11:44:28Z
date_published: 2018-10-01T00:00:00Z
date_updated: 2023-10-10T13:11:29Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
- _id: JaMa
doi: 10.30757/ALEA.v15-49
ec_funded: 1
external_id:
arxiv:
- '1705.08836'
isi:
- '000460475800022'
file:
- access_level: open_access
checksum: 2ded46aa284a836a8cbb34133a64f1cb
content_type: application/pdf
creator: kschuh
date_created: 2019-02-14T09:44:10Z
date_updated: 2020-07-14T12:47:46Z
file_id: '5981'
file_name: 2018_ALEA_Nejjar.pdf
file_size: 394851
relation: main_file
file_date_updated: 2020-07-14T12:47:46Z
has_accepted_license: '1'
intvolume: ' 15'
isi: 1
issue: '2'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 1311-1334
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Latin American Journal of Probability and Mathematical Statistics
publication_identifier:
issn:
- 1980-0436
publication_status: published
publisher: Instituto Nacional de Matematica Pura e Aplicada
quality_controlled: '1'
scopus_import: '1'
status: public
title: Transition to shocks in TASEP and decoupling of last passage times
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 15
year: '2018'
...
---
_id: '75'
abstract:
- lang: eng
text: We prove that any convex body in the plane can be partitioned into m convex
parts of equal areas and perimeters for any integer m≥2; this result was previously
known for prime powers m=pk. We also give a higher-dimensional generalization.
article_number: '1804.03057'
article_processing_charge: No
arxiv: 1
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Sergey
full_name: Avvakumov, Sergey
id: 3827DAC8-F248-11E8-B48F-1D18A9856A87
last_name: Avvakumov
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
citation:
ama: Akopyan A, Avvakumov S, Karasev R. Convex fair partitions into arbitrary number
of pieces. 2018. doi:10.48550/arXiv.1804.03057
apa: Akopyan, A., Avvakumov, S., & Karasev, R. (2018). Convex fair partitions
into arbitrary number of pieces. arXiv. https://doi.org/10.48550/arXiv.1804.03057
chicago: Akopyan, Arseniy, Sergey Avvakumov, and Roman Karasev. “Convex Fair Partitions
into Arbitrary Number of Pieces.” arXiv, 2018. https://doi.org/10.48550/arXiv.1804.03057.
ieee: A. Akopyan, S. Avvakumov, and R. Karasev, “Convex fair partitions into arbitrary
number of pieces.” arXiv, 2018.
ista: Akopyan A, Avvakumov S, Karasev R. 2018. Convex fair partitions into arbitrary
number of pieces. 1804.03057.
mla: Akopyan, Arseniy, et al. Convex Fair Partitions into Arbitrary Number of
Pieces. 1804.03057, arXiv, 2018, doi:10.48550/arXiv.1804.03057.
short: A. Akopyan, S. Avvakumov, R. Karasev, (2018).
date_created: 2018-12-11T11:44:30Z
date_published: 2018-09-13T00:00:00Z
date_updated: 2023-12-18T10:51:02Z
day: '13'
department:
- _id: HeEd
- _id: JaMa
doi: 10.48550/arXiv.1804.03057
ec_funded: 1
external_id:
arxiv:
- '1804.03057'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1804.03057
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication_status: published
publisher: arXiv
related_material:
record:
- id: '8156'
relation: dissertation_contains
status: public
status: public
title: Convex fair partitions into arbitrary number of pieces
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2018'
...
---
_id: '556'
abstract:
- lang: eng
text: 'We investigate the free boundary Schur process, a variant of the Schur process
introduced by Okounkov and Reshetikhin, where we allow the first and the last
partitions to be arbitrary (instead of empty in the original setting). The pfaffian
Schur process, previously studied by several authors, is recovered when just one
of the boundary partitions is left free. We compute the correlation functions
of the process in all generality via the free fermion formalism, which we extend
with the thorough treatment of “free boundary states.” For the case of one free
boundary, our approach yields a new proof that the process is pfaffian. For the
case of two free boundaries, we find that the process is not pfaffian, but a closely
related process is. We also study three different applications of the Schur process
with one free boundary: fluctuations of symmetrized last passage percolation models,
limit shapes and processes for symmetric plane partitions and for plane overpartitions.'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Dan
full_name: Betea, Dan
last_name: Betea
- first_name: Jeremie
full_name: Bouttier, Jeremie
last_name: Bouttier
- first_name: Peter
full_name: Nejjar, Peter
id: 4BF426E2-F248-11E8-B48F-1D18A9856A87
last_name: Nejjar
- first_name: Mirjana
full_name: Vuletic, Mirjana
last_name: Vuletic
citation:
ama: Betea D, Bouttier J, Nejjar P, Vuletic M. The free boundary Schur process and
applications I. Annales Henri Poincare. 2018;19(12):3663-3742. doi:10.1007/s00023-018-0723-1
apa: Betea, D., Bouttier, J., Nejjar, P., & Vuletic, M. (2018). The free boundary
Schur process and applications I. Annales Henri Poincare. Springer Nature.
https://doi.org/10.1007/s00023-018-0723-1
chicago: Betea, Dan, Jeremie Bouttier, Peter Nejjar, and Mirjana Vuletic. “The Free
Boundary Schur Process and Applications I.” Annales Henri Poincare. Springer
Nature, 2018. https://doi.org/10.1007/s00023-018-0723-1.
ieee: D. Betea, J. Bouttier, P. Nejjar, and M. Vuletic, “The free boundary Schur
process and applications I,” Annales Henri Poincare, vol. 19, no. 12. Springer
Nature, pp. 3663–3742, 2018.
ista: Betea D, Bouttier J, Nejjar P, Vuletic M. 2018. The free boundary Schur process
and applications I. Annales Henri Poincare. 19(12), 3663–3742.
mla: Betea, Dan, et al. “The Free Boundary Schur Process and Applications I.” Annales
Henri Poincare, vol. 19, no. 12, Springer Nature, 2018, pp. 3663–742, doi:10.1007/s00023-018-0723-1.
short: D. Betea, J. Bouttier, P. Nejjar, M. Vuletic, Annales Henri Poincare 19 (2018)
3663–3742.
date_created: 2018-12-11T11:47:09Z
date_published: 2018-11-13T00:00:00Z
date_updated: 2024-02-20T10:48:17Z
day: '13'
ddc:
- '500'
department:
- _id: LaEr
- _id: JaMa
doi: 10.1007/s00023-018-0723-1
ec_funded: 1
external_id:
arxiv:
- '1704.05809'
file:
- access_level: open_access
checksum: 0c38abe73569b7166b7487ad5d23cc68
content_type: application/pdf
creator: dernst
date_created: 2019-01-21T15:18:55Z
date_updated: 2020-07-14T12:47:03Z
file_id: '5866'
file_name: 2018_Annales_Betea.pdf
file_size: 3084674
relation: main_file
file_date_updated: 2020-07-14T12:47:03Z
has_accepted_license: '1'
intvolume: ' 19'
issue: '12'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 3663-3742
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Annales Henri Poincare
publication_identifier:
issn:
- 1424-0637
publication_status: published
publisher: Springer Nature
publist_id: '7258'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The free boundary Schur process and applications I
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 19
year: '2018'
...
---
_id: '6355'
abstract:
- lang: eng
text: We prove that any cyclic quadrilateral can be inscribed in any closed convex
C1-curve. The smoothness condition is not required if the quadrilateral is a
rectangle.
article_number: e7
article_processing_charge: No
arxiv: 1
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Sergey
full_name: Avvakumov, Sergey
id: 3827DAC8-F248-11E8-B48F-1D18A9856A87
last_name: Avvakumov
citation:
ama: Akopyan A, Avvakumov S. Any cyclic quadrilateral can be inscribed in any closed
convex smooth curve. Forum of Mathematics, Sigma. 2018;6. doi:10.1017/fms.2018.7
apa: Akopyan, A., & Avvakumov, S. (2018). Any cyclic quadrilateral can be inscribed
in any closed convex smooth curve. Forum of Mathematics, Sigma. Cambridge
University Press. https://doi.org/10.1017/fms.2018.7
chicago: Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be
Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma.
Cambridge University Press, 2018. https://doi.org/10.1017/fms.2018.7.
ieee: A. Akopyan and S. Avvakumov, “Any cyclic quadrilateral can be inscribed in
any closed convex smooth curve,” Forum of Mathematics, Sigma, vol. 6. Cambridge
University Press, 2018.
ista: Akopyan A, Avvakumov S. 2018. Any cyclic quadrilateral can be inscribed in
any closed convex smooth curve. Forum of Mathematics, Sigma. 6, e7.
mla: Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed
in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma, vol. 6,
e7, Cambridge University Press, 2018, doi:10.1017/fms.2018.7.
short: A. Akopyan, S. Avvakumov, Forum of Mathematics, Sigma 6 (2018).
date_created: 2019-04-30T06:09:57Z
date_published: 2018-05-31T00:00:00Z
date_updated: 2023-09-19T14:50:12Z
day: '31'
ddc:
- '510'
department:
- _id: UlWa
- _id: HeEd
- _id: JaMa
doi: 10.1017/fms.2018.7
ec_funded: 1
external_id:
arxiv:
- '1712.10205'
isi:
- '000433915500001'
file:
- access_level: open_access
checksum: 5a71b24ba712a3eb2e46165a38fbc30a
content_type: application/pdf
creator: dernst
date_created: 2019-04-30T06:14:58Z
date_updated: 2020-07-14T12:47:28Z
file_id: '6356'
file_name: 2018_ForumMahtematics_Akopyan.pdf
file_size: 249246
relation: main_file
file_date_updated: 2020-07-14T12:47:28Z
has_accepted_license: '1'
intvolume: ' 6'
isi: 1
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Forum of Mathematics, Sigma
publication_identifier:
issn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
related_material:
record:
- id: '8156'
relation: dissertation_contains
status: public
status: public
title: Any cyclic quadrilateral can be inscribed in any closed convex smooth curve
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 6
year: '2018'
...
---
_id: '1215'
abstract:
- lang: eng
text: "Two generalizations of Itô formula to infinite-dimensional spaces are given.\r\nThe
first one, in Hilbert spaces, extends the classical one by taking advantage of\r\ncancellations
when they occur in examples and it is applied to the case of a group\r\ngenerator.
The second one, based on the previous one and a limit procedure, is an Itô\r\nformula
in a special class of Banach spaces having a product structure with the noise\r\nin
a Hilbert component; again the key point is the extension due to a cancellation.
This\r\nextension to Banach spaces and in particular the specific cancellation
are motivated\r\nby path-dependent Itô calculus."
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). The second named author benefited partially from the support of the
“FMJH Program Gaspard Monge in Optimization and Operations Research” (Project 2014-1607H).
He is also grateful for the invitation to the Department of Mathematics of the University
of Pisa. The third named author is grateful for the invitation to ENSTA.
article_processing_charge: Yes (via OA deal)
author:
- first_name: Franco
full_name: Flandoli, Franco
last_name: Flandoli
- first_name: Francesco
full_name: Russo, Francesco
last_name: Russo
- first_name: Giovanni A
full_name: Zanco, Giovanni A
id: 47491882-F248-11E8-B48F-1D18A9856A87
last_name: Zanco
citation:
ama: Flandoli F, Russo F, Zanco GA. Infinite-dimensional calculus under weak spatial
regularity of the processes. Journal of Theoretical Probability. 2018;31(2):789-826.
doi:10.1007/s10959-016-0724-2
apa: Flandoli, F., Russo, F., & Zanco, G. A. (2018). Infinite-dimensional calculus
under weak spatial regularity of the processes. Journal of Theoretical Probability.
Springer. https://doi.org/10.1007/s10959-016-0724-2
chicago: Flandoli, Franco, Francesco Russo, and Giovanni A Zanco. “Infinite-Dimensional
Calculus under Weak Spatial Regularity of the Processes.” Journal of Theoretical
Probability. Springer, 2018. https://doi.org/10.1007/s10959-016-0724-2.
ieee: F. Flandoli, F. Russo, and G. A. Zanco, “Infinite-dimensional calculus under
weak spatial regularity of the processes,” Journal of Theoretical Probability,
vol. 31, no. 2. Springer, pp. 789–826, 2018.
ista: Flandoli F, Russo F, Zanco GA. 2018. Infinite-dimensional calculus under weak
spatial regularity of the processes. Journal of Theoretical Probability. 31(2),
789–826.
mla: Flandoli, Franco, et al. “Infinite-Dimensional Calculus under Weak Spatial
Regularity of the Processes.” Journal of Theoretical Probability, vol.
31, no. 2, Springer, 2018, pp. 789–826, doi:10.1007/s10959-016-0724-2.
short: F. Flandoli, F. Russo, G.A. Zanco, Journal of Theoretical Probability 31
(2018) 789–826.
date_created: 2018-12-11T11:50:45Z
date_published: 2018-06-01T00:00:00Z
date_updated: 2021-01-12T06:49:09Z
day: '01'
ddc:
- '519'
department:
- _id: JaMa
doi: 10.1007/s10959-016-0724-2
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intvolume: ' 31'
issue: '2'
language:
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month: '06'
oa: 1
oa_version: Published Version
page: 789-826
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Journal of Theoretical Probability
publication_status: published
publisher: Springer
publist_id: '6119'
pubrep_id: '712'
quality_controlled: '1'
scopus_import: 1
status: public
title: Infinite-dimensional calculus under weak spatial regularity of the processes
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 31
year: '2018'
...
---
_id: '560'
abstract:
- lang: eng
text: In a recent article (Jentzen et al. 2016 Commun. Math. Sci. 14, 1477–1500
(doi:10.4310/CMS.2016.v14. n6.a1)), it has been established that, for every arbitrarily
slow convergence speed and every natural number d ? {4, 5, . . .}, there exist
d-dimensional stochastic differential equations with infinitely often differentiable
and globally bounded coefficients such that no approximation method based on finitely
many observations of the driving Brownian motion can converge in absolute mean
to the solution faster than the given speed of convergence. In this paper, we
strengthen the above result by proving that this slow convergence phenomenon also
arises in two (d = 2) and three (d = 3) space dimensions.
article_number: '0104'
author:
- first_name: Mate
full_name: Gerencser, Mate
id: 44ECEDF2-F248-11E8-B48F-1D18A9856A87
last_name: Gerencser
- first_name: Arnulf
full_name: Jentzen, Arnulf
last_name: Jentzen
- first_name: Diyora
full_name: Salimova, Diyora
last_name: Salimova
citation:
ama: 'Gerencser M, Jentzen A, Salimova D. On stochastic differential equations with
arbitrarily slow convergence rates for strong approximation in two space dimensions.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering
Sciences. 2017;473(2207). doi:10.1098/rspa.2017.0104'
apa: 'Gerencser, M., Jentzen, A., & Salimova, D. (2017). On stochastic differential
equations with arbitrarily slow convergence rates for strong approximation in
two space dimensions. Proceedings of the Royal Society A: Mathematical, Physical
and Engineering Sciences. Royal Society of London. https://doi.org/10.1098/rspa.2017.0104'
chicago: 'Gerencser, Mate, Arnulf Jentzen, and Diyora Salimova. “On Stochastic Differential
Equations with Arbitrarily Slow Convergence Rates for Strong Approximation in
Two Space Dimensions.” Proceedings of the Royal Society A: Mathematical, Physical
and Engineering Sciences. Royal Society of London, 2017. https://doi.org/10.1098/rspa.2017.0104.'
ieee: 'M. Gerencser, A. Jentzen, and D. Salimova, “On stochastic differential equations
with arbitrarily slow convergence rates for strong approximation in two space
dimensions,” Proceedings of the Royal Society A: Mathematical, Physical and
Engineering Sciences, vol. 473, no. 2207. Royal Society of London, 2017.'
ista: 'Gerencser M, Jentzen A, Salimova D. 2017. On stochastic differential equations
with arbitrarily slow convergence rates for strong approximation in two space
dimensions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering
Sciences. 473(2207), 0104.'
mla: 'Gerencser, Mate, et al. “On Stochastic Differential Equations with Arbitrarily
Slow Convergence Rates for Strong Approximation in Two Space Dimensions.” Proceedings
of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.
473, no. 2207, 0104, Royal Society of London, 2017, doi:10.1098/rspa.2017.0104.'
short: 'M. Gerencser, A. Jentzen, D. Salimova, Proceedings of the Royal Society
A: Mathematical, Physical and Engineering Sciences 473 (2017).'
date_created: 2018-12-11T11:47:11Z
date_published: 2017-11-01T00:00:00Z
date_updated: 2021-01-12T08:03:04Z
day: '01'
department:
- _id: JaMa
doi: 10.1098/rspa.2017.0104
ec_funded: 1
intvolume: ' 473'
issue: '2207'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1702.03229
month: '11'
oa: 1
oa_version: Submitted Version
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: 'Proceedings of the Royal Society A: Mathematical, Physical and Engineering
Sciences'
publication_identifier:
issn:
- '13645021'
publication_status: published
publisher: Royal Society of London
publist_id: '7256'
quality_controlled: '1'
scopus_import: 1
status: public
title: On stochastic differential equations with arbitrarily slow convergence rates
for strong approximation in two space dimensions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 473
year: '2017'
...