Arnulf Jentzen
TitleCited byYear
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
2412011
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
2212012
Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
M Hutzenthaler, A Jentzen
American Mathematical Society 236 (1112), 2015
1502015
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
132*2018
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 …, 2008
1232008
The numerical approximation of stochastic partial differential equations
A Jentzen, PE Kloeden
Milan Journal of Mathematics 77 (1), 205-244, 2009
1162009
Taylor approximations for stochastic partial differential equations
A Jentzen, PE Kloeden
SIAM, 2011
1142011
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
752011
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
68*2017
Galerkin approximations for the stochastic Burgers equation
D Blomker, A Jentzen
SIAM Journal on Numerical Analysis 51 (1), 694-715, 2013
68*2013
Pathwise approximation of stochastic differential equations on domains: higher order convergence rates without global Lipschitz coefficients
A Jentzen, PE Kloeden, A Neuenkirch
Numerische Mathematik 112 (1), 41-64, 2009
682009
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
642011
On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with non-globally monotone coefficients
M Hutzenthaler, A Jentzen
arXiv preprint arXiv:1401.0295, 2014
632014
Pathwise numerical approximations of SPDEs with additive noise under non-global Lipschitz coefficients
A Jentzen
Potential Analysis 31 (4), 375, 2009
632009
Loss of regularity for Kolmogorov equations
M Hairer, M Hutzenthaler, A Jentzen
The Annals of Probability 43 (2), 468-527, 2015
622015
Regularity analysis for stochastic partial differential equations with nonlinear multiplicative trace class noise
A Jentzen, M Röckner
arXiv preprint arXiv:1005.4095, 2010
612010
A mild Itô formula for SPDEs
G Da Prato, A Jentzen, M Röckner
Transactions of the American Mathematical Society, 2019
492019
Taylor expansions of solutions of stochastic partial differential equations with additive noise
A Jentzen, P Kloeden
The Annals of Probability 38 (2), 532-569, 2010
492010
A Milstein scheme for SPDEs
A Jentzen, M Röckner
Arxiv preprint arXiv:1001.2751, 2010
47*2010
Higher order pathwise numerical approximations of SPDEs with additive noise
A Jentzen
SIAM Journal on Numerical Analysis 49 (2), 642-667, 2011
442011
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Articles 1–20