Now in its second edition, this book gives a systematic and self-contained presentation of
basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and …

Many stochastic differential equations (SDEs) in the literature have a superlinearly growing
nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the …

In his forward-looking paper [374] at the conference “Mathematics Towards the Third
Millennium,” our esteemed colleague at Brown University Prof. David Mumford argued that …

This monograph grew out of my Ph. D. thesis, which I wrote at Bielefeld University between
2008 and 2012. Its main objective is the analysis of numerical methods, which approximate …

Abstract We introduce Functional Diffusion Processes (FDPs), which generalize score-
based diffusion models to infinite-dimensional function spaces. FDPs require a new …

The numerical solution of stochastic partial differential equations (SPDEs) is at a stage of
development roughly similar to that of stochastic ordinary differential equations (SODEs) in …

Strong and weak approximation errors of a spatial finite element method are analyzed for
the stochastic partial differential equations (SPDEs) with one-sided Lipschitz coefficients …

We consider Galerkin finite element methods for semilinear stochastic partial differential
equations (SPDEs) with multiplicative noise and Lipschitz continuous nonlinearities. We …

Abstract In Becker and Jentzen (2019) and Becker et al.(2017), an explicit temporal semi-
discretization scheme and a space–time full-discretization scheme were, respectively …

We introduce and analyze an explicit time discretization scheme for the one-dimensional
stochastic Allen-Cahn, driven by space-time white noise. The scheme is based on a splitting …