443 citations · 2.4k across the 59 of their papers we have counts for
7 papers · 1 filter
Strong convergence rates for full-discrete approximations of stochastic Burgers equations with multiplicative noise
Martin Hutzenthaler, Robert Link
In this article we establish strong convergence rates on the whole probability space for explicit full-discrete approximations of stochastic Burgers equations with multiplicative t…
A path-dependent stochastic Gronwall inequality and strong convergence rate for stochastic functional differential equations
Martin Hutzenthaler, Tuan Anh Nguyen
We derive a stochastic Gronwall lemma with suprema over the paths in the upper bound of the assumed affine-linear growth assumption. This allows applications to Itô processes with…
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
We prove that deep neural networks are capable of approximating solutions of semilinear Kolmogorov PDE in the case of gradient-independent, Lipschitz-continuous nonlinearities, whi…
Stopped Brownian-increment tamed Euler method
Martin Hutzenthaler, Kai Kisker
In this article we propose a new explicit Euler-type approximation method for stochastic differential equations (SDEs). In this method, Brownian increments in the recursion of the…
Multilevel Picard approximations for high-dimensional decoupled forward-backward stochastic differential equations
Martin Hutzenthaler, Tuan Anh Nguyen
Backward stochastic differential equations (BSDEs) appear in numeruous applications. Classical approximation methods suffer from the curse of dimensionality and deep learning-based…
The Kolmogorov backward equation for stochastic Burgers equations and for stochastic 2D-Navier-Stokes equations
Martin Hutzenthaler, Robert Link
In this book we establish under suitable assumptions the uniqueness and existence of viscosity solutions of Kolmogorov backward equations for stochastic partial differential equati…
Multilevel Picard approximations of high-dimensional semilinear partial differential equations with locally monotone coefficient functions
Martin Hutzenthaler, Tuan Anh Nguyen
The full history recursive multilevel Picard approximation method for semilinear parabolic partial differential equations (PDEs) is the only method which provably overcomes the cur…