443 citations · 2.4k across the 59 of their papers we have counts for
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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…
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…