Martin Hutzenthaler

发表

An overview on deep learning-based approximation methods for partial differential equations

M. Hutzenthaler, Arnulf Jentzen, C. Beck, 2020, Discrete and Continuous Dynamical Systems - B.

Numerical Approximations of Stochastic Differential Equations With Non-globally Lipschitz Continuous Coefficients

M. Hutzenthaler, Arnulf Jentzen, Martin Hutzenthaler, 2012, 1203.5809.

Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients

P. Kloeden, M. Hutzenthaler, Arnulf Jentzen, 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

Norovirus GII.4 and GII.7 capsid sequences undergo positive selection in chronically infected patients.

M. Hutzenthaler, D. Metzler, U. Protzer, 2012, Infection, genetics and evolution : journal of molecular epidemiology and evolutionary genetics in infectious diseases.

Deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear partial differential equations

M. Hutzenthaler, Petru A. Cioica-Licht, P. Werner, 2022, ArXiv.

Differentiability of semigroups of stochastic differential equations with Hölder-continuous diffusion coefficients

M. Hutzenthaler, D. Pieper, Martin Hutzenthaler, 2018, 1803.10608.

Time reversal of some stationary jump diffusion processes from population genetics

M. Hutzenthaler, J. Taylor, Martin Hutzenthaler, 2010, Advances in Applied Probability.

Overcoming the curse of dimensionality in the numerical approximation of Allen–Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations

Arnulf Jentzen, Thomas Kruse, Christian Beck, 2019, J. Num. Math..

Local Lipschitz continuity in the initial value and strong completeness for nonlinear stochastic differential equations

M. Hutzenthaler, Arnulf Jentzen, S. Cox, 2013, 1309.5595.

A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations

Arnulf Jentzen, T. Kruse, T. Nguyen, 2019, SN Partial Differential Equations and Applications.

Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations

Arnulf Jentzen, Thomas Kruse, Martin Hutzenthaler, 2018, Proceedings of the Royal Society A.

On nonlinear Feynman-Kac formulas for viscosity solutions of semilinear parabolic partial differential equations with gradient-dependent nonlinearities

Martin Hutzenthaler, Katharina Pohl, 2023, 2310.18197.

On nonlinear Feynman–Kac formulas for viscosity solutions of semilinear parabolic partial differential equations

Arnulf Jentzen, Martin Hutzenthaler, Christian Beck, 2020, Stochastics and Dynamics.

On the It\^o-Alekseev-Gr\"obner formula for stochastic differential equations

M. Hutzenthaler, Arnulf Jentzen, Sara Mazzonetto, 2018, 1812.09857.

Multilevel Picard iterations for solving smooth semilinear parabolic heat equations

W. E, M. Hutzenthaler, Arnulf Jentzen, 2016, Partial Differential Equations and Applications.

On full history recursive multilevel Picard approximations and numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations

E Weinan, Arnulf Jentzen, Thomas Kruse, 2016 .

Strong convergence rates and temporal regularity for Cox-Ingersoll-Ross processes and Bessel processes with accessible boundaries

M. Hutzenthaler, Arnulf Jentzen, Marco Noll, 2014, 1403.6385.

On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with non-globally monotone coefficients

M. Hutzenthaler, Arnulf Jentzen, Martin Hutzenthaler, 2014, 1401.0295.

Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations

Peter E. Kloeden, Arnulf Jentzen, Martin Hutzenthaler, 2011, 1105.0226.

Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients

P. Kloeden, Arnulf Jentzen, Martin Hutzenthaler, 2010, 1010.3756.

Convergence of the Stochastic Euler Scheme for Locally Lipschitz Coefficients

Arnulf Jentzen, Martin Hutzenthaler, M. Hutzenthaler, 2009, Found. Comput. Math..

Altruistic defense traits in structured populations

M. Hutzenthaler, D. Metzler, F. Jordan, 2015 .

Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations

Xiaojie Wang, Arnulf Jentzen, Martin Hutzenthaler, 2013, Math. Comput..

Interacting diffusions and trees of excursions: convergence and comparison

M. Hutzenthaler, Martin Hutzenthaler, 2011, 1104.1060.

Stopped Brownian-increment tamed Euler method

M. Hutzenthaler, Kai Kisker, Martin Hutzenthaler, 2022, ArXiv.

Multilevel Picard approximations of high-dimensional semilinear partial differential equations with locally monotone coefficient functions

M. Hutzenthaler, T. Nguyen, Martin Hutzenthaler, 2022, Applied Numerical Mathematics.

Strong convergence rate of Euler-Maruyama approximations in temporal-spatial Hölder-norms

M. Hutzenthaler, T. Nguyen, Martin Hutzenthaler, 2021, J. Comput. Appl. Math..

Strong convergence rates on the whole probability space for space-time discrete numerical approximation schemes for stochastic Burgers equations

Arnulf Jentzen, F. Lindner, Primož Pušnik, 2019, ArXiv.

Existence of spatially differentiable solutions of stochastic differential equations with non-globally monotone coefficient functions

M. Hutzenthaler, Sara Mazzonetto, Anselm Hudde, 2019 .

A stochastic Gronwall inequality and applications to moments, strong completeness, strong local Lipschitz continuity, and perturbations

Martin Hutzenthaler, Sara Mazzonetto, M. Hutzenthaler, 2019, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques.

Strong and weak divergence of exponential and linear-implicit Euler approximations for stochastic partial differential equations with superlinearly growing nonlinearities

M. Hutzenthaler, Arnulf Jentzen, Diyora Salimova, 2019, 1903.06066.

On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations

E Weinan, Arnulf Jentzen, Thomas Kruse, 2017, Journal of Scientific Computing.

Linear scaling algorithms for solving high-dimensional nonlinear parabolic differential equations

E. Weinan, M. Hutzenthaler, Arnulf Jentzen, 2016 .

Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions

M. Hutzenthaler, Arnulf Jentzen, S. Cox, 2016, IMA Journal of Numerical Analysis.

Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equations

Arnulf Jentzen, Martin Hutzenthaler, Diyora Salimova, 2016, 1604.02053.

Loss of regularity for Kolmogorov equations

Martin Hairer, Arnulf Jentzen, Martin Hutzenthaler, 2012, 1209.6035.

Non-globally Lipschitz Counterexamples for the stochastic Euler scheme

Arnulf Jentzen, Martin Hutzenthaler, 2009 .

The Virgin Island Model

Martin Hutzenthaler, M. Hutzenthaler, Martin Hutzenthaler, 2008, 0802.3145.

Selection for altruistic defense in structured populations

M. Hutzenthaler, D. Metzler, F. Jordan, 2019, bioRxiv.

Branching diffusions in random environment

M. Hutzenthaler, Christian Boinghoff, Martin Hutzenthaler, 2011, 1107.2773.

Supercritical branching diffusions in random environment

M. Hutzenthaler, Martin Hutzenthaler, 2011, 1109.1849.

Multilevel Picard approximations for high-dimensional decoupled forward-backward stochastic differential equations

M. Hutzenthaler, T. Nguyen, Martin Hutzenthaler, 2022, ArXiv.

Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations pdf

Arnulf Jentzen, Thomas Kruse, Martin Hutzenthaler, 2021, J. Num. Math..

Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks

Philippe von Wurstemberger, M. Hutzenthaler, Arnulf Jentzen, 2019, Electronic Journal of Probability.

Multilevel Picard approximations for McKean-Vlasov stochastic differential equations

T. Kruse, T. Nguyen, Martin Hutzenthaler, 2021, Journal of Mathematical Analysis and Applications.

Propagation of chaos and the many-demes limit for weakly interacting diffusions in the sparse regime

M. Hutzenthaler, D. Pieper, Martin Hutzenthaler, 2018, 1804.01034.

Survival, extinction and ergodicity in a spatially continuous population model

N. Berestycki, M. Hutzenthaler, Martin Hutzenthaler, 2009 .

Overcoming the Curse of Dimensionality in the Numerical Approximation of Parabolic Partial Differential Equations with Gradient-Dependent Nonlinearities pdf

Arnulf Jentzen, Thomas Kruse, Martin Hutzenthaler, 2019, Foundations of Computational Mathematics.

Ecological and genetic effects of introduced species on their native competitors.

Meike J. Wittmann, W. Gabriel, M. Hutzenthaler, 2012, Theoretical population biology.

Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions

M. Hutzenthaler, Arnulf Jentzen, Luca Scarpa, 2021, ArXiv.

Full history recursive multilevel Picard approximations for ordinary differential equations with expectations pdf

Arnulf Jentzen, Martin Hutzenthaler, Christian Beck, 2021, ArXiv.

On full history recursive multilevel Picard approximations and numerical approximations of high-dimensional nonlinear parabolic partial differential equations

E. Weinan, M. Hutzenthaler, Arnulf Jentzen, 2016 .