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

By Jianbo Cui, Jialin Hong, Liying Sun. Stochastic Processes and their Applications, 2018

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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.

Subfields: Demography, Finance, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/cc5d2aa2e4c75ce5be1968de7babee231c1de5ed