Non-uniform Discretizations for Strong Approximation of SPDEs

Klaus Ritter, TU Kaiserslautern

Abstract: Stochastic partial differential equations (SPDEs) give rise to various computational problems like strong and weak approximation as well as cubature, i.e., approximation of trajectories and their distributions, resp., as well as computation of expectations of functionals.
Commonly used algorithms often employ a uniform discretization in time and space.

In this talk we discuss the power of non-uniform discretization for strong approximation of certain
SPDEs, and we also point to comparable results for stochastic ordinary differential equations.
In particular, spatially adaptive wavelet algorithms are studied for a stochastic Poisson equation, where the stochastic model of the right-hand side permits sparsity of the wavelet coefficients.

Supported by the DFG within the SPP 1324.