English

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

Numerical Analysis 2018-12-19 v1

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

Keywords

Cite

@article{arxiv.1812.07419,
  title  = {Pathwise space approximations of semi-linear parabolic SPDEs with multiplicative noise},
  author = {Sonja Cox and Erika Hausenblas},
  journal= {arXiv preprint arXiv:1812.07419},
  year   = {2018}
}

Comments

This article was published in the International Journal of Computer Mathematics in December 2012. However, the proof of Proposition 4.2 in the published article contained a mistake in the final estimate. This mistake is repaired in the arXiv submission (see Proposition 4.1), all changes with respect to the published article are marked red. The mistake did not affect the main results