---
_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.
    <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering
    Sciences</i>. 2017;473(2207). doi:<a href="https://doi.org/10.1098/rspa.2017.0104">10.1098/rspa.2017.0104</a>'
  apa: 'Gerencser, M., Jentzen, A., &#38; Salimova, D. (2017). On stochastic differential
    equations with arbitrarily slow convergence rates for strong approximation in
    two space dimensions. <i>Proceedings of the Royal Society A: Mathematical, Physical
    and Engineering Sciences</i>. Royal Society of London. <a href="https://doi.org/10.1098/rspa.2017.0104">https://doi.org/10.1098/rspa.2017.0104</a>'
  chicago: 'Gerencser, Mate, Arnulf Jentzen, and Diyora Salimova. “On Stochastic Differential
    Equations with Arbitrarily Slow Convergence Rates for Strong Approximation in
    Two Space Dimensions.” <i>Proceedings of the Royal Society A: Mathematical, Physical
    and Engineering Sciences</i>. Royal Society of London, 2017. <a href="https://doi.org/10.1098/rspa.2017.0104">https://doi.org/10.1098/rspa.2017.0104</a>.'
  ieee: 'M. Gerencser, A. Jentzen, and D. Salimova, “On stochastic differential equations
    with arbitrarily slow convergence rates for strong approximation in two space
    dimensions,” <i>Proceedings of the Royal Society A: Mathematical, Physical and
    Engineering Sciences</i>, 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.” <i>Proceedings
    of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>, vol.
    473, no. 2207, 0104, Royal Society of London, 2017, doi:<a href="https://doi.org/10.1098/rspa.2017.0104">10.1098/rspa.2017.0104</a>.'
  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'
...