443 citations · 2.4k across the 59 of their papers we have counts for
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On the Itô-Alekseev-Gröbner formula for stochastic differential equations
Anselm Hudde, Martin Hutzenthaler, Arnulf Jentzen +1
In this article we establish a new formula for the difference of a test function of the solution of a stochastic differential equation and of the test function of an Itô process. T…
Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations
Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse +2
For a long time it is well-known that high-dimensional linear parabolic partial differential equations (PDEs) can be approximated by Monte Carlo methods with a computational effort…
Propagation of chaos and the many-demes limit for weakly interacting diffusions in the sparse regime
Martin Hutzenthaler, Daniel Pieper
Propagation of chaos is a well-studied phenomenon and shows that weakly interacting diffusions may become independent as the system size converges to infinity. Most of the literatu…
Differentiability of semigroups of stochastic differential equations with Hölder-continuous diffusion coefficients
Martin Hutzenthaler, Daniel Pieper
Differentiability of semigroups is useful for many applications. Here we focus on stochastic differential equations whose diffusion coefficient is the square root of a differentiab…