Convergence of the Stochastic Euler Scheme for Locally Lipschitz Coefficients. - Martin Hutzenthaler; Arnulf Jentzen (Found. Comput. Math., 2011)

Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations. - Martin Hutzenthaler; Arnulf Jentzen; Xiaojie Wang 007 (Math. Comput., 2018)

Strong convergence rates on the whole probability space for space-time discrete numerical approximation schemes for stochastic Burgers equations. - Martin Hutzenthaler; Arnulf Jentzen; Felix Lindner 002; Primoz Pusnik (CoRR, 2019)

On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations. - Weinan E; Martin Hutzenthaler; Arnulf Jentzen; Thomas Kruse (J. Sci. Comput., 2019)

Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations. - Sebastian Becker; Ramon Braunwarth; Martin Hutzenthaler; Arnulf Jentzen; Philippe von Wurstemberger (CoRR, 2020)

Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities. - Martin Hutzenthaler; Arnulf Jentzen; Thomas Kruse; Tuan Anh Nguyen (CoRR, 2020)

An overview on deep learning-based approximation methods for partial differential equations. - Christian Beck; Martin Hutzenthaler; Arnulf Jentzen; Benno Kuckuck (CoRR, 2020)

Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations. - Christian Beck; Fabian Hornung; Martin Hutzenthaler; Arnulf Jentzen; Thomas Kruse (J. Num. Math., 2020)

Multilevel Picard Approximations of High-Dimensional Semilinear Parabolic Differential Equations with Gradient-Dependent Nonlinearities. - Martin Hutzenthaler; Thomas Kruse (SIAM J. Numer. Anal., 2020)

Full history recursive multilevel Picard approximations for ordinary differential equations with expectations. - Christian Beck; Martin Hutzenthaler; Arnulf Jentzen; Emilia Magnani (CoRR, 2021)

Multilevel Picard approximations for McKean-Vlasov stochastic differential equations. - Martin Hutzenthaler; Thomas Kruse; Tuan Anh Nguyen (CoRR, 2021)

Strong Lp-error analysis of nonlinear Monte Carlo approximations for high-dimensional semilinear partial differential equations. - Martin Hutzenthaler; Arnulf Jentzen; Benno Kuckuck; Joshua Lee Padgett (CoRR, 2021)

Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions. - Martin Hutzenthaler; Arnulf Jentzen; Katharina Pohl; Adrian Riekert; Luca Scarpa (CoRR, 2021)

Multilevel Picard approximations of high-dimensional semilinear partial differential equations with locally monotone coefficient functions. - Tuan Anh Nguyen; Martin Hutzenthaler (CoRR, 2022)

Multilevel Picard approximations for high-dimensional decoupled forward-backward stochastic differential equations. - Martin Hutzenthaler; Tuan Anh Nguyen (CoRR, 2022)

Stopped Brownian-increment tamed Euler method. - Martin Hutzenthaler; Kai Kisker (CoRR, 2022)

Deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear partial differential equations. - Petru A. Cioica-Licht; Martin Hutzenthaler; P. Tobias Werner (CoRR, 2022)

Overcoming the Curse of Dimensionality in the Numerical Approximation of Parabolic Partial Differential Equations with Gradient-Dependent Nonlinearities. - Martin Hutzenthaler; Arnulf Jentzen; Thomas Kruse (Found. Comput. Math., 2022)

Strong convergence rate of Euler-Maruyama approximations in temporal-spatial Hölder-norms. - Martin Hutzenthaler; Tuan Anh Nguyen (J. Comput. Appl. Math., 2022)

Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations. - Martin Hutzenthaler; Arnulf Jentzen; Thomas Kruse; Tuan Anh Nguyen (J. Num. Math., 2023)

Full history recursive multilevel Picard approximations suffer from the curse of dimensionality for the Hamilton-Jacobi-Bellman equation of a stochastic control problem. - Martin Hutzenthaler; Tuan Anh Nguyen (CoRR, 2025)