Analysis of an exponential integrator for stochastic PDEs driven by Riesz noise

Abstract

We present and study an explicit exponential integrator for parabolic SPDEs in any dimension driven by a Gaussian noise which is white in time and with spatial correlation given by a Riesz kernel. Under assumptions on the coefficients of the SPDE, we prove strong error bounds and exhibit how the rate of convergence depends on the exponent in the Riesz kernel. Finally, numerical experiments in spatial dimensions $1$ and $2$ are provided in order to confirm our convergence results.