Martin Hutzenthaler

Publication Activity (10 Years)

Years Active: 2011-2023
Publications (10 Years): 23

Top Topics

Approximation Schemes

Convergence Proof

Problems In Image Processing

Top Venues

SIAM J. Numer. Anal.

J. Comput. Appl. Math.

Publications

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) (2023)
Tuan Anh Nguyen, Martin Hutzenthaler
Multilevel Picard approximations of high-dimensional semilinear partial differential equations with locally monotone coefficient functions. CoRR (2022)
Martin Hutzenthaler, Kai Kisker
Stopped Brownian-increment tamed Euler method. CoRR (2022)
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 (2022)
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) (2022)
Martin Hutzenthaler, Tuan Anh Nguyen
Multilevel Picard approximations for high-dimensional decoupled forward-backward stochastic differential equations. CoRR (2022)
Martin Hutzenthaler, Tuan Anh Nguyen
Strong convergence rate of Euler-Maruyama approximations in temporal-spatial Hölder-norms. J. Comput. Appl. Math. 413 (2022)
Martin Hutzenthaler, Arnulf Jentzen, Benno Kuckuck, Joshua Lee Padgett
-error analysis of nonlinear Monte Carlo approximations for high-dimensional semilinear partial differential equations. CoRR (2021)
Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse, Tuan Anh Nguyen
Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations. CoRR (2021)
Tuan Anh Nguyen, Martin Hutzenthaler
Strong convergence rate of Euler-Maruyama approximations in temporal-spatial Hölder-norms. CoRR (2021)
Martin Hutzenthaler, Thomas Kruse, Tuan Anh Nguyen
Multilevel Picard approximations for McKean-Vlasov stochastic differential equations. CoRR (2021)
Christian Beck, Martin Hutzenthaler, Arnulf Jentzen, Emilia Magnani
Full history recursive multilevel Picard approximations for ordinary differential equations with expectations. CoRR (2021)
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 (2021)
Christian Beck, Martin Hutzenthaler, Arnulf Jentzen, Benno Kuckuck
An overview on deep learning-based approximation methods for partial differential equations. CoRR (2020)
Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse, Tuan Anh Nguyen
Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities. CoRR (2020)
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 (2020)
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) (2020)
Martin Hutzenthaler, Thomas Kruse
Multilevel Picard Approximations of High-Dimensional Semilinear Parabolic Differential Equations with Gradient-Dependent Nonlinearities. SIAM J. Numer. Anal. 58 (2) (2020)
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 (2019)
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 (2019)
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) (2019)
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 (2019)
Martin Hutzenthaler, Arnulf Jentzen, Xiaojie Wang
Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations. Math. Comput. 87 (311) (2018)
Martin Hutzenthaler, Arnulf Jentzen
Convergence of the Stochastic Euler Scheme for Locally Lipschitz Coefficients. Found. Comput. Math. 11 (6) (2011)