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Journal Articles
- 2023
[j8]Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse, Tuan Anh Nguyen:
Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations. J. Num. Math. 31(1): 1-28 (2023)- 2022
- [j7]Martin Hutzenthaler, Arnulf Jentzen
, Thomas Kruse:
Overcoming the Curse of Dimensionality in the Numerical Approximation of Parabolic Partial Differential Equations with Gradient-Dependent Nonlinearities. Found. Comput. Math. 22(4): 905-966 (2022) - [j6]Martin Hutzenthaler, Tuan Anh Nguyen:
Strong convergence rate of Euler-Maruyama approximations in temporal-spatial Hölder-norms. J. Comput. Appl. Math. 413: 114391 (2022) - 2020
- [j5]Christian Beck, Fabian Hornung, Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse:
Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations. J. Num. Math. 28(4): 197-222 (2020) - [j4]Martin Hutzenthaler, Thomas Kruse:
Multilevel Picard Approximations of High-Dimensional Semilinear Parabolic Differential Equations with Gradient-Dependent Nonlinearities. SIAM J. Numer. Anal. 58(2): 929-961 (2020) - 2019
- [j3]Weinan E, Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse:
On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations. J. Sci. Comput. 79(3): 1534-1571 (2019) - 2018
- [j2]Martin Hutzenthaler, Arnulf Jentzen, Xiaojie Wang:
Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations. Math. Comput. 87(311): 1353-1413 (2018) - 2011
- [j1]Martin Hutzenthaler, Arnulf Jentzen:
Convergence of the Stochastic Euler Scheme for Locally Lipschitz Coefficients. Found. Comput. Math. 11(6): 657-706 (2011)
Informal and Other Publications
- 2022
- [i16]Tuan Anh Nguyen, Martin Hutzenthaler:
Multilevel Picard approximations of high-dimensional semilinear partial differential equations with locally monotone coefficient functions. CoRR abs/2202.02582 (2022) - [i15]Martin Hutzenthaler, Tuan Anh Nguyen:
Multilevel Picard approximations for high-dimensional decoupled forward-backward stochastic differential equations. CoRR abs/2204.08511 (2022) - [i14]Martin Hutzenthaler, Kai Kisker:
Stopped Brownian-increment tamed Euler method. CoRR abs/2204.12254 (2022) - [i13]Petru A. Cioica-Licht, Martin Hutzenthaler, P. Tobias Werner:
Deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear partial differential equations. CoRR abs/2205.14398 (2022) - 2021
- [i12]Christian Beck, Martin Hutzenthaler, Arnulf Jentzen, Emilia Magnani:
Full history recursive multilevel Picard approximations for ordinary differential equations with expectations. CoRR abs/2103.02350 (2021) - [i11]Martin Hutzenthaler, Thomas Kruse, Tuan Anh Nguyen:
Multilevel Picard approximations for McKean-Vlasov stochastic differential equations. CoRR abs/2103.10870 (2021) - [i10]Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse, Tuan Anh Nguyen:
Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations. CoRR abs/2108.10602 (2021) - [i9]Martin Hutzenthaler, Arnulf Jentzen, Benno Kuckuck, Joshua Lee Padgett:
Strong Lp-error analysis of nonlinear Monte Carlo approximations for high-dimensional semilinear partial differential equations. CoRR abs/2110.08297 (2021) - [i8]Tuan Anh Nguyen, Martin Hutzenthaler:
Strong convergence rate of Euler-Maruyama approximations in temporal-spatial Hölder-norms. CoRR abs/2111.04630 (2021) - [i7]Martin Hutzenthaler, Arnulf Jentzen, Katharina Pohl, Adrian Riekert, Luca Scarpa:
Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions. CoRR abs/2112.07369 (2021) - 2020
- [i6]Sebastian Becker, Ramon Braunwarth, Martin Hutzenthaler, Arnulf Jentzen, Philippe von Wurstemberger:
Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations. CoRR abs/2005.10206 (2020) - [i5]Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse, Tuan Anh Nguyen:
Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities. CoRR abs/2009.02484 (2020) - [i4]Christian Beck, Martin Hutzenthaler, Arnulf Jentzen, Benno Kuckuck:
An overview on deep learning-based approximation methods for partial differential equations. CoRR abs/2012.12348 (2020) - 2019
- [i3]Christian Beck, Fabian Hornung, Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse:
Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations. CoRR abs/1907.06729 (2019) - [i2]Martin Hutzenthaler, Arnulf Jentzen, Felix Lindner, Primoz Pusnik:
Strong convergence rates on the whole probability space for space-time discrete numerical approximation schemes for stochastic Burgers equations. CoRR abs/1911.01870 (2019) - [i1]Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse:
Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities. CoRR abs/1912.02571 (2019)
Coauthor Index
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