An exponential Wagner-Platen type scheme for SPDEs
Abstract
The strong numerical approximation of semilinear stochastic partial differential equations (SPDEs) driven by infinite dimensional Wiener processes is investigated. There are a number of results in the literature that show that Euler-type approximation methods converge strongly, under suitable assumptions, to the exact solutions of such SPDEs with strong order 1/2 or at least with strong order 1/2 - epsilon where epsilon > 0 is arbitrarily small. Recent results extend these results and show that Milstein-type approximation methods converge, under suitable assumptions, to the exact solutions of such SPDEs with strong order 1 - epsilon. It has also been shown that splitting-up approximation methods converge, under suitable assumptions, with strong order 1 to the exact solutions of such SPDEs. In this article an exponential Wagner-Platen type numerical approximation method for such SPDEs is proposed and shown to converge, under suitable assumptions, with strong order 3/2 - epsilon to the exact solutions of such SPDEs.
Cite
@article{arxiv.1309.4648,
title = {An exponential Wagner-Platen type scheme for SPDEs},
author = {Sebastian Becker and Arnulf Jentzen and Peter E. Kloeden},
journal= {arXiv preprint arXiv:1309.4648},
year = {2021}
}