We use the scale of Besov spaces B^\alpha_ {\tau,\tau}(O),\alpha> 0, 1/\tau=\alpha/d+ 1/p, p
fixed, to study the spatial regularity of the solutions of linear parabolic stochastic partial …

Rough differential equations are solved for signals in general Besov spaces unifying in
particular the known results in Hölder and p-variation topology. To this end the …

Abstract Quasi–Monte Carlo (QMC) integration of output functionals of solutions of the
diffusion problem with a log-normal random coefficient is considered. The random coefficient …

We characterize the local smoothness and the asymptotic growth rate of the Lévy white
noise. We do so by characterizing the weighted Besov spaces in which it is located. We …

We investigate the regularity of linear stochastic parabolic equations with zero Dirichlet
boundary condition on bounded Lipschitz domains O⊂R^d with both theoretical and …

We consider the semilinear stochastic heat equation perturbed by additive noise. After time-
discretization by Euler's method the equation is split into a linear stochastic equation and a …

Stochastic partial differential equations (SPDEs, for short) are the mathematical models of
choice for space time evolutions corrupted by noise. Although in many settings it is known …

This paper addresses the problem of regularity properties of functions represented as an
expansion in a wavelet basis with random coefficients in terms of finiteness of their Besov …

We review a series of results that have been obtained in the context of the DFG-SPP 1324
project “Adaptive wavelet methods for SPDEs”. This project has been concerned with the …

This paper is concerned with the construction of random functions on bounded domains
which possess a well-defined, prescribed smoothness in specific function spaces. In …