Weak convergence and invariant measure of a full discretization for parabolic SPDEs with non-globally Lipschitz coefficients

Jianbo Cui, Jialin Hong, Liying Sun

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)

Abstract

We propose a full discretization to approximate the invariant measure numerically for parabolic stochastic partial differential equations (SPDEs) with non-globally Lipschitz coefficients. We present a priori estimates and regularity estimates of the numerical solution via a variational approach and Malliavin calculus. Under certain hypotheses, we present the time-independent regularity estimates for the corresponding Kolmogorov equation and the time-independent weak convergence analysis for the full discretization. Furthermore, we show that the V-uniformly ergodic invariant measure of the original system is approximated by this full discretization with weak convergence rate. Numerical experiments verify theoretical findings.

Original languageEnglish
Pages (from-to)55-93
Number of pages39
JournalStochastic Processes and their Applications
Volume134
DOIs
Publication statusPublished - Apr 2021
Externally publishedYes

Keywords

  • Invariant measure
  • Kolmogorov equation
  • Malliavin calculus
  • Weak convergence

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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