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

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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 min⁡{1−𝛿,2−2⁢𝛾}, for some 0<𝛿<1 and 0<𝛾<1/2.

Details

Original languageEnglish
Pages (from-to)3029-3048
Number of pages19
JournalApplicable Analysis
Volume103.2024
Issue number16
DOIs
Publication statusPublished - 19 Mar 2024