Approximating stochastic evolution equations with additive white and rough noises

Yanzhao Cao, Jialin Hong, Zhihui Liu*

*Corresponding author for this work

Research output: Contribution to journalJournal Articlepeer-review

Abstract

In this paper, we analyze Galerkin approximations for stochastic evolution equations driven by an additive Gaussian noise which is temporally white and spatially fractional with Hurst index less than or equal to 1=2. First we regularize the noise by the Wong-Zakai approximation and obtain its optimal order of convergence. Then we apply the Galerkin method to discretize the stochastic evolution equations with regularized noises. Optimal error estimates are obtained for the Galerkin approximations. In particular, our error estimates remove an infinitesimal factor which appears in the error estimates of various numerical methods for stochastic evolution equations in existing literatures.

Original languageEnglish
Pages (from-to)1958-1981
Number of pages24
JournalSIAM Journal on Numerical Analysis
Volume55
Issue number4
DOIs
Publication statusPublished - 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017 Society for Industrial and Applied Mathematics.

Keywords

  • Fractional Brownian motion
  • Galerkin approximation
  • Stochastic evolution equation
  • Wong-Zakai approximation

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