Born: October 1993 (age 27)
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Education
| 03/2019-08/2019 | Research stay at the Mathematical Institute, University of Oxford, in the research group of Prof. Dr. Mike Giles |
| 10/2018-02/2019 | Research stay at the Faculty of Mathematics, University of Vienna, in the research group of Prof. Dr. Philipp Grohs |
| 06/2015-05/2020 | PhD student at the Seminar for Applied Mathematics, ETH Zürich, in the research group of Prof. Dr. Arnulf Jentzen |
| 05/2015 | Master degree in Mathematics, ETH Zürich |
| 09/2014 | Bachelor degree in Mathematics, ETH Zürich |
| 08/2013-01/2014 | Term abroad at NUS (Singapore) |
| 08/2010 | Matura at the Mathematisch-Naturwissenschaftliches Gymnasium Rämibühl |
Preprints
(authors listed in alphabetical order)
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Jentzen, A. and Welti, T., Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisation. [arXiv] (2020), 51 pages.
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Giles, M. B., Jentzen, A., and Welti, T., Generalised multilevel Picard approximations. [arXiv] (2019), 61 pages. Revision requested from IMA J. Numer. Anal.
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Becker, S., Cheridito, P., Jentzen, A., and Welti, T., Solving high-dimensional optimal stopping problems using deep learning. [arXiv] (2019), 42 pages. Revision requested from European J. Appl. Math.
Published or accepted research articles
(authors listed in alphabetical order)
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Jentzen, A., Salimova, D., and Welti, T., A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients. [arXiv] (2018), 48 pages. Accepted in Commun. Math. Sci.
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Jentzen, A., Salimova, D., and Welti, T., Strong convergence for explicit space–time discrete numerical approximation methods for stochastic Burgers equations. J. Math. Anal. Appl. 469 (2019), no. 2, 661-704. [arXiv]
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Jacobe de Naurois, L., Jentzen, A., and Welti, T., Lower Bounds for Weak Approximation Errors for Spatial Spectral Galerkin Approximations of Stochastic Wave Equations. In: Stochastic Partial Differential Equations and Related Fields Springer International Publishing, Cham, 2018, 237-248. [arXiv]
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Andersson, A., Jentzen, A., Kurniawan, R., and Welti, T., On the differentiability of solutions of stochastic evolution equations with respect to their initial values. Nonlinear Anal. 162 (2017), 128-161. [arXiv]
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Cox, S., Hutzenthaler, M., Jentzen, A., van Neerven, J., and Welti, T., Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions. [arXiv] (2016), 48 pages. To appear in IMA J. Numer. Anal.
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Jacobe de Naurois, L., Jentzen, A., and Welti, T., Weak convergence rates for spatial spectral Galerkin approximations of semilinear stochastic wave equations with multiplicative noise. [arXiv] (2015), 27 pages. Accepted in Appl. Math. Optim.