443 citations · 2.4k across the 59 of their papers we have counts for
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On nonlinear Feynman-Kac formulas for viscosity solutions of semilinear parabolic partial differential equations with gradient-dependent nonlinearities
Martin Hutzenthaler, Katharina Pohl
The classical Feynman-Kac identity represents solutions of linear partial differential equations in terms of stochastic differential euqations. This representation has been general…
On existence and uniqueness properties for solutions of stochastic fixed point equations with gradient-dependent nonlinearities
Katharina Pohl, Martin Hutzenthaler
The combination of the Itô formula and the Bismut-Elworthy-Li formula implies that suitable smooth solutions of semilinear Kolmogorov partial differential equations (PDEs) are also…
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…