Pathwise space approximations of semi-linear parabolic SPDEs with multiplicative noise

Abstract

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 almost sure uniform convergence, i.e. pathwise convergence. The proofs are based on a recent perturbation result for such equations.

Keywords:

• stochastic differential equations
• stochastic partial differential equations
• perturbation
• spectral Galerkin method
• finite-element approximation

2010 AMS Subject Classifications:

• 35R60
• 60H15
• 60H35
• 65M15
• 65M60

Acknowledgements

The authors wish to thank Jan van Neerven for helpful comments.