Wong–Zakai approximation of a stochastic partial differential equation with multiplicative noise

Erika Hausenblas, Tsiry Avisoa Randrianasolo

Research output: Contribution to journalArticleResearchpeer-review

Abstract

In this article, we derive the convergence rate for the Wong–Zakai equation of some approximation of stochastic evolution equations with multiplicative noise. To be more precise, the diffusion coefficient in front of the noise is the multiplication operator, and, is therefore not bounded, a situation not treated in the literature. Since our motivation comes from problems in numerical ling, we consider a finite, high-dimensional problem approximating a stochastic evolution equation on a random time grid. By imposing suitable stability conditions on the drift term and the time grid, we achieve a convergence rate in the mean square of order (Formula presented.), for some (Formula presented.) and (Formula presented.).

Original languageEnglish
JournalApplicable Analysis
Volume2024
Issue number??? Stand: 26. März 2024
DOIs
Publication statusPublished - 19 Mar 2024

Bibliographical note

Publisher Copyright:
© 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.

Keywords

  • 60J65
  • 65C30
  • multiplicative noise
  • partial differential equations with randomness
  • Primary 35R60
  • Secondary 65M15
  • Stochastic partial differential equations
  • time-discretization scheme
  • Wong–Zakai approximation

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