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An exponential Wagner-Platen type scheme for SPDEs

by S. Becker and A. Jentzen and P. Kloeden

(Report number 2013-36)

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.

Keywords: semilinear stochastic partial differential equations, semlinear SPDEs, Wagner-Platen scheme for SPDEs, higher order convergence

@Techreport{BJK13_533,
  author = {S. Becker and A. Jentzen and P. Kloeden},
  title = {An exponential Wagner-Platen type scheme for SPDEs},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2013-36},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2013/2013-36.pdf },
  year = {2013}
}

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