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Arnulf Jentzen
Arnulf Jentzen
Chinese University of Hong Kong, Shenzhen & University of Muenster
Verified email at uni-muenster.de - Homepage
Title
Cited by
Cited by
Year
Solving high-dimensional partial differential equations using deep learning
J Han, A Jentzen, E Weinan
Proceedings of the National Academy of Sciences 115 (34), 8505-8510, 2018
8542018
Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
W E, J Han, A Jentzen
https://arxiv.org/abs/1706.04702, 2017
412*2017
Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
M Hutzenthaler, A Jentzen, PE Kloeden
Proceedings of the Royal Society A: Mathematical, Physical and Engineering …, 2011
3612011
Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
M Hutzenthaler, A Jentzen, PE Kloeden
The Annals of Applied Probability 22 (4), 1611-1641, 2012
3482012
Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
M Hutzenthaler, A Jentzen
American Mathematical Soc., 2015
2202015
Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space–time noise
A Jentzen, PE Kloeden
Proceedings of the Royal Society A: Mathematical, Physical and Engineering …, 2009
1652009
Taylor approximations for stochastic partial differential equations
A Jentzen, PE Kloeden
Society for Industrial and Applied Mathematics, 2011
1562011
The numerical approximation of stochastic partial differential equations
A Jentzen, PE Kloeden
Milan Journal of Mathematics 77 (1), 205-244, 2009
1522009
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations
P Grohs, F Hornung, A Jentzen, P Von Wurstemberger
arXiv preprint arXiv:1809.02362, 2018
1472018
Deep optimal stopping
S Becker, P Cheridito, A Jentzen
arXiv preprint arXiv:1804.05394, 2018
1442018
Analysis of the generalization error: Empirical risk minimization over deep artificial neural networks overcomes the curse of dimensionality in the numerical approximation of …
J Berner, P Grohs, A Jentzen
SIAM Journal on Mathematics of Data Science 2 (3), 631-657, 2020
1262020
Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations
C Beck, A Jentzen
Journal of Nonlinear Science 29 (4), 1563-1619, 2019
1222019
Solving the Kolmogorov PDE by means of deep learning
C Beck, S Becker, P Grohs, N Jaafari, A Jentzen
Journal of Scientific Computing 88 (3), 1-28, 2021
1172021
A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations
M Hutzenthaler, A Jentzen, T Kruse, TA Nguyen
SN partial differential equations and applications 1 (2), 1-34, 2020
1072020
On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients
M Hutzenthaler, A Jentzen
The Annals of Probability 48 (1), 53-93, 2020
1002020
Loss of regularity for Kolmogorov equations
M Hairer, M Hutzenthaler, A Jentzen
The Annals of Probability 43 (2), 468-527, 2015
952015
Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations
M Hutzenthaler, A Jentzen, PE Kloeden
Arxiv preprint arXiv:1105.0226, 2011
912011
Galerkin approximations for the stochastic Burgers equation
D Blomker, A Jentzen
SIAM Journal on Numerical Analysis 51 (1), 694-715, 2013
89*2013
Regularity analysis for stochastic partial differential equations with nonlinear multiplicative trace class noise
A Jentzen, M Röckner
arXiv preprint arXiv:1005.4095, 2010
852010
A Milstein scheme for SPDEs
A Jentzen, M Röckner
Arxiv preprint arXiv:1001.2751, 2010
83*2010
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