Arnulf Jentzen
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Zitiert von
Jahr
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
6612018
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
3392011
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
3292012
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
322*2017
Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
M Hutzenthaler, A Jentzen
American Mathematical Soc., 2015
2052015
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
1572009
Taylor approximations for stochastic partial differential equations
A Jentzen, PE Kloeden
Society for Industrial and Applied Mathematics, 2011
1522011
The numerical approximation of stochastic partial differential equations
A Jentzen, PE Kloeden
Milan Journal of Mathematics 77 (1), 205-244, 2009
1482009
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
1242018
Deep optimal stopping
S Becker, P Cheridito, A Jentzen
Journal of Machine Learning Research 20, 74, 2019
1122019
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
952020
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
942020
Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations
C Beck, E Weinan, A Jentzen
Journal of Nonlinear Science 29 (4), 1563-1619, 2019
942019
Loss of regularity for Kolmogorov equations
M Hairer, M Hutzenthaler, A Jentzen
The Annals of Probability 43 (2), 468-527, 2015
932015
Solving stochastic differential equations and Kolmogorov equations by means of deep learning
C Beck, S Becker, P Grohs, N Jaafari, A Jentzen
arXiv preprint arXiv:1806.00421, 2018
912018
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
882011
Galerkin approximations for the stochastic Burgers equation
D Blomker, A Jentzen
SIAM Journal on Numerical Analysis 51 (1), 694-715, 2013
86*2013
Regularity analysis for stochastic partial differential equations with nonlinear multiplicative trace class noise
A Jentzen, M Röckner
arXiv preprint arXiv:1005.4095, 2010
862010
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
832020
Efficient simulation of nonlinear parabolic SPDEs with additive noise
A Jentzen, P Kloeden, G Winkel
The Annals of Applied Probability 21 (3), 908-950, 2011
802011
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