Följ
Arnulf Jentzen
Arnulf Jentzen
The Chinese University of Hong Kong, Shenzhen & University of Münster
Verifierad e-postadress på uni-muenster.de - Startsida
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Solving high-dimensional partial differential equations using deep learning
J Han, A Jentzen, W E
Proceedings of the National Academy of Sciences 115 (34), 8505-8510, 2018
16752018
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
699*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
4872011
Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
M Hutzenthaler, A Jentzen, PE Kloeden
4712012
Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
M Hutzenthaler, A Jentzen
American Mathematical Society 236 (1112), 2015
2712015
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
Memoirs of the American Mathematical Society 284, 1-106, 2023
2472023
Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations
C Beck, W E, A Jentzen
Journal of Nonlinear Science 29, 1563-1619, 2019
2412019
Deep optimal stopping
S Becker, P Cheridito, A Jentzen
Journal of Machine Learning Research 20 (74), 1-25, 2019
2342019
Solving the Kolmogorov PDE by means of deep learning
C Beck, S Becker, P Grohs, N Jaafari, A Jentzen
Journal of Scientific Computing 88, 1-28, 2021
1932021
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
1922020
Taylor approximations for stochastic partial differential equations
A Jentzen, PE Kloeden
Society for Industrial and Applied Mathematics, 2011
1892011
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
1872009
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), 10, 2020
1812020
The numerical approximation of stochastic partial differential equations
A Jentzen, PE Kloeden
Milan Journal of Mathematics 77, 205-244, 2009
1762009
Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning
E Weinan, J Han, A Jentzen
Nonlinearity 35 (1), 278, 2021
1372021
A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant …
A Jentzen, D Salimova, T Welti
arXiv preprint arXiv:1809.07321, 2018
1372018
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
1362020
Deep splitting method for parabolic PDEs
C Beck, S Becker, P Cheridito, A Jentzen, A Neufeld
SIAM Journal on Scientific Computing 43 (5), A3135-A3154, 2021
1352021
An overview on deep learning-based approximation methods for partial differential equations
C Beck, M Hutzenthaler, A Jentzen, B Kuckuck
arXiv preprint arXiv:2012.12348, 2020
1342020
DNN expression rate analysis of high-dimensional PDEs: Application to option pricing
D Elbrächter, P Grohs, A Jentzen, C Schwab
Constructive Approximation 55 (1), 3-71, 2022
1272022
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Artiklar 1–20