Pathwise space approximations of semi-linear parabolic SPDEs with multiplicative noise
For researchers in numerical analysis of SPDEs, this work offers rigorous convergence rates for pathwise approximations, though it is incremental as it extends existing perturbation techniques.
This paper provides convergence rates for spectral Galerkin and finite element approximations of semi-linear parabolic SPDEs with multiplicative noise, establishing strong and almost sure uniform (pathwise) convergence. The rates are derived using a previously published perturbation result.
We provide convergence rates for space approximations of semi-linear stochastic differential equations with multiplicative noise in a Hilbert space. The space approximations we consider are spectral Galerkin and finite elements, and the type of convergence we consider is strong and almost sure uniform convergence, i.e., pathwise convergence. The proofs are based on a previously published perturbation result for such equations.