---
_id: '7388'
abstract:
- lang: eng
text: We give a Wong-Zakai type characterisation of the solutions of quasilinear
heat equations driven by space-time white noise in 1 + 1 dimensions. In order
to show that the renormalisation counterterms are local in the solution, a careful
arrangement of a few hundred terms is required. The main tool in this computation
is a general ‘integration by parts’ formula that provides a number of linear identities
for the renormalisation constants.
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
citation:
ama: Gerencser M. Nondivergence form quasilinear heat equations driven by space-time
white noise. Annales de l’Institut Henri Poincaré C, Analyse non linéaire.
2020;37(3):663-682. doi:10.1016/j.anihpc.2020.01.003
apa: Gerencser, M. (2020). Nondivergence form quasilinear heat equations driven
by space-time white noise. Annales de l’Institut Henri Poincaré C, Analyse
Non Linéaire. Elsevier. https://doi.org/10.1016/j.anihpc.2020.01.003
chicago: Gerencser, Mate. “Nondivergence Form Quasilinear Heat Equations Driven
by Space-Time White Noise.” Annales de l’Institut Henri Poincaré C, Analyse
Non Linéaire. Elsevier, 2020. https://doi.org/10.1016/j.anihpc.2020.01.003.
ieee: M. Gerencser, “Nondivergence form quasilinear heat equations driven by space-time
white noise,” Annales de l’Institut Henri Poincaré C, Analyse non linéaire,
vol. 37, no. 3. Elsevier, pp. 663–682, 2020.
ista: Gerencser M. 2020. Nondivergence form quasilinear heat equations driven by
space-time white noise. Annales de l’Institut Henri Poincaré C, Analyse non linéaire.
37(3), 663–682.
mla: Gerencser, Mate. “Nondivergence Form Quasilinear Heat Equations Driven by Space-Time
White Noise.” Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire,
vol. 37, no. 3, Elsevier, 2020, pp. 663–82, doi:10.1016/j.anihpc.2020.01.003.
short: M. Gerencser, Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire
37 (2020) 663–682.
date_created: 2020-01-29T09:39:41Z
date_published: 2020-05-01T00:00:00Z
date_updated: 2023-08-17T14:35:46Z
day: '01'
department:
- _id: JaMa
doi: 10.1016/j.anihpc.2020.01.003
external_id:
arxiv:
- '1902.07635'
isi:
- '000531049800007'
intvolume: ' 37'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1902.07635
month: '05'
oa: 1
oa_version: Preprint
page: 663-682
publication: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
publication_identifier:
issn:
- 0294-1449
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Nondivergence form quasilinear heat equations driven by space-time white noise
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 37
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: '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: '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: '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'
...
---
_id: '642'
abstract:
- lang: eng
text: Cauchy problems with SPDEs on the whole space are localized to Cauchy problems
on a ball of radius R. This localization reduces various kinds of spatial approximation
schemes to finite dimensional problems. The error is shown to be exponentially
small. As an application, a numerical scheme is presented which combines the localization
and the space and time discretization, and thus is fully implementable.
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. Localization errors in solving stochastic partial differential
equations in the whole space. Mathematics of Computation. 2017;86(307):2373-2397.
doi:10.1090/mcom/3201
apa: Gerencser, M., & Gyöngy, I. (2017). Localization errors in solving stochastic
partial differential equations in the whole space. Mathematics of Computation.
American Mathematical Society. https://doi.org/10.1090/mcom/3201
chicago: Gerencser, Mate, and István Gyöngy. “Localization Errors in Solving Stochastic
Partial Differential Equations in the Whole Space.” Mathematics of Computation.
American Mathematical Society, 2017. https://doi.org/10.1090/mcom/3201.
ieee: M. Gerencser and I. Gyöngy, “Localization errors in solving stochastic partial
differential equations in the whole space,” Mathematics of Computation,
vol. 86, no. 307. American Mathematical Society, pp. 2373–2397, 2017.
ista: Gerencser M, Gyöngy I. 2017. Localization errors in solving stochastic partial
differential equations in the whole space. Mathematics of Computation. 86(307),
2373–2397.
mla: Gerencser, Mate, and István Gyöngy. “Localization Errors in Solving Stochastic
Partial Differential Equations in the Whole Space.” Mathematics of Computation,
vol. 86, no. 307, American Mathematical Society, 2017, pp. 2373–97, doi:10.1090/mcom/3201.
short: M. Gerencser, I. Gyöngy, Mathematics of Computation 86 (2017) 2373–2397.
date_created: 2018-12-11T11:47:40Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2021-01-12T08:07:26Z
day: '01'
department:
- _id: JaMa
doi: 10.1090/mcom/3201
intvolume: ' 86'
issue: '307'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1508.05535
month: '01'
oa: 1
oa_version: Submitted Version
page: 2373 - 2397
publication: Mathematics of Computation
publication_identifier:
issn:
- '00255718'
publication_status: published
publisher: American Mathematical Society
publist_id: '7144'
quality_controlled: '1'
scopus_import: 1
status: public
title: Localization errors in solving stochastic partial differential equations in
the whole space
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 86
year: '2017'
...