BibTeX

preprints.bib

@misc{https://doi.org/10.48550/arxiv.2111.00215,
  doi = {10.48550/ARXIV.2111.00215},
  url = {https://arxiv.org/abs/2111.00215},
  author = {Baggenstos, Jonas and Salimova, Diyora},
  title = {Approximation properties of Residual Neural Networks for Kolmogorov PDEs},
  publisher = {arXiv},
  year = {2021},
  copyright = {arXiv.org perpetual, non-exclusive license}
}

@misc{https://doi.org/10.48550/arxiv.2007.02723,
  doi = {10.48550/ARXIV.2007.02723},
  url = {https://arxiv.org/abs/2007.02723},
  author = {Bercher, Aritz and Gonon, Lukas and Jentzen, Arnulf and Salimova, Diyora},
  title = {Weak error analysis for stochastic gradient descent optimization algorithms},
  publisher = {arXiv},
  year = {2020},
  copyright = {arXiv.org perpetual, non-exclusive license}
}

@misc{https://doi.org/10.48550/arxiv.2006.02199,
  doi = {10.48550/ARXIV.2006.02199},
  url = {https://arxiv.org/abs/2006.02199},
  author = {Hornung, Fabian and Jentzen, Arnulf and Salimova, Diyora},
  title = {Space-time deep neural network approximations for high-dimensional partial differential equations},
  publisher = {arXiv},
  year = {2020},
  copyright = {arXiv.org perpetual, non-exclusive license}
}

@misc{https://doi.org/10.48550/arxiv.1908.10828,
  doi = {10.48550/ARXIV.1908.10828},
  url = {https://arxiv.org/abs/1908.10828},
  author = {Grohs, Philipp and Jentzen, Arnulf and Salimova, Diyora},
  title = {Deep neural network approximations for Monte Carlo algorithms},
  publisher = {arXiv},
  year = {2019},
  copyright = {arXiv.org perpetual, non-exclusive license}
}

@misc{https://doi.org/10.48550/arxiv.1903.06066,
  doi = {10.48550/ARXIV.1903.06066},
  url = {https://arxiv.org/abs/1903.06066},
  author = {Beccari, Matteo and Hutzenthaler, Martin and Jentzen, Arnulf and Kurniawan, Ryan and Lindner, Felix and Salimova, Diyora},
  title = {Strong and weak divergence of exponential and linear-implicit Euler approximations for stochastic partial differential equations with superlinearly growing nonlinearities},
  publisher = {arXiv},
  year = {2019},
  copyright = {arXiv.org perpetual, non-exclusive license}
}

@misc{https://doi.org/10.48550/arxiv.1812.06859,
  doi = {10.48550/ARXIV.1812.06859},
  url = {https://arxiv.org/abs/1812.06859},
  author = {Jentzen, Arnulf and Mazzonetto, Sara and Salimova, Diyora},
  title = {Existence and uniqueness properties for solutions of a class of Banach space valued evolution equations},
  publisher = {arXiv},
  year = {2018},
  copyright = {arXiv.org perpetual, non-exclusive license}
}

articles.bib

@article{MR4283528,
  author = {Jentzen, Arnulf and Salimova, Diyora and Welti, Timo},
  title = {A proof that deep artificial neural networks overcome the
              curse of dimensionality in the numerical approximation of
              {K}olmogorov partial differential equations with constant
              diffusion and nonlinear drift coefficients},
  journal = {Commun. Math. Sci.},
  fjournal = {Communications in Mathematical Sciences},
  volume = {19},
  year = {2021},
  number = {5},
  pages = {1167--1205},
  issn = {1539-6746},
  mrclass = {65M99 (68T05)},
  mrnumber = {4283528},
  doi = {10.4310/CMS.2021.v19.n5.a1},
  url = {https://doi.org/10.4310/CMS.2021.v19.n5.a1}
}

@article{MR4112739,
  author = {Mazzonetto, Sara and Salimova, Diyora},
  title = {Existence, uniqueness, and numerical approximations for
              stochastic {B}urgers equations},
  journal = {Stoch. Anal. Appl.},
  fjournal = {Stochastic Analysis and Applications},
  volume = {38},
  year = {2020},
  number = {4},
  pages = {623--646},
  issn = {0736-2994},
  mrclass = {60H15 (35Q53 35R60 60H35)},
  mrnumber = {4112739},
  mrreviewer = {Ali Zakaria},
  doi = {10.1080/07362994.2019.1709503},
  url = {https://doi.org/10.1080/07362994.2019.1709503}
}

@article{MR3860443,
  author = {Jentzen, Arnulf and Salimova, Diyora and Welti, Timo},
  title = {Strong convergence for explicit space-time discrete numerical
              approximation methods for stochastic {B}urgers equations},
  journal = {J. Math. Anal. Appl.},
  fjournal = {Journal of Mathematical Analysis and Applications},
  volume = {469},
  year = {2019},
  number = {2},
  pages = {661--704},
  issn = {0022-247X},
  mrclass = {60H35 (35Q53 35R60 65M75)},
  mrnumber = {3860443},
  mrreviewer = {Romeo I. Negrea},
  doi = {10.1016/j.jmaa.2018.09.032},
  url = {https://doi.org/10.1016/j.jmaa.2018.09.032}
}

@article{MR3919602,
  author = {Hutzenthaler, Martin and Jentzen, Arnulf and Salimova, Diyora},
  title = {Strong convergence of full-discrete nonlinearity-truncated
              accelerated exponential {E}uler-type approximations for
              stochastic {K}uramoto-{S}ivashinsky equations},
  journal = {Commun. Math. Sci.},
  fjournal = {Communications in Mathematical Sciences},
  volume = {16},
  year = {2018},
  number = {6},
  pages = {1489--1529},
  issn = {1539-6746},
  mrclass = {60H35 (35Q53 35R60)},
  mrnumber = {3919602},
  doi = {10.4310/CMS.2018.v16.n6.a2},
  url = {https://doi.org/10.4310/CMS.2018.v16.n6.a2}
}

@article{MR3741822,
  author = {Gerencs\'{e}r, M\'{a}t\'{e} and Jentzen, Arnulf and Salimova, Diyora},
  title = {On stochastic differential equations with arbitrarily slow
              convergence rates for strong approximation in two space
              dimensions},
  journal = {Proc. A.},
  fjournal = {Proceedings A},
  volume = {473},
  year = {2017},
  number = {2207},
  pages = {20170104, 16},
  issn = {1364-5021},
  mrclass = {60H10 (34F05)},
  mrnumber = {3741822},
  mrreviewer = {Daniel C. Biles},
  doi = {10.1098/rspa.2017.0104},
  url = {https://doi.org/10.1098/rspa.2017.0104}
}

@article{MR3338637,
  author = {Ibragimov, Zarif O. and Salimova, Diyora F.},
  title = {On an inequality in {$l_p(\Bbb{C})$} involving {B}asel
              problem},
  journal = {Elem. Math.},
  fjournal = {Elemente der Mathematik},
  volume = {70},
  year = {2015},
  number = {2},
  pages = {79--81},
  issn = {0013-6018},
  mrclass = {26D15},
  mrnumber = {3338637},
  doi = {10.4171/EM/278},
  url = {https://doi.org/10.4171/EM/278}
}