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

Jianbo Cui, Jialin Hong and Liying Sun

Stochastic Processes and their Applications, 2021, vol. 134, issue C, 55-93

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.

Keywords: Weak convergence; Invariant measure; Kolmogorov equation; Malliavin calculus (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:134:y:2021:i:c:p:55-93

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DOI: 10.1016/j.spa.2020.12.003

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