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

Author

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  • Cui, Jianbo
  • Hong, Jialin
  • Sun, Liying

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.

Suggested Citation

  • Cui, Jianbo & Hong, Jialin & Sun, Liying, 2021. "Weak convergence and invariant measure of a full discretization for parabolic SPDEs with non-globally Lipschitz coefficients," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 55-93.
    • Handle: RePEc:eee:spapps:v:134:y:2021:i:c:p:55-93
    DOI: 10.1016/j.spa.2020.12.003
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    References listed on IDEAS

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    1. Becker, Sebastian & Jentzen, Arnulf, 2019. "Strong convergence rates for nonlinearity-truncated Euler-type approximations of stochastic Ginzburg–Landau equations," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 28-69.
    2. Wang, Xiaojie, 2020. "An efficient explicit full-discrete scheme for strong approximation of stochastic Allen–Cahn equation," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6271-6299.
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    Cited by:

    1. Chen, Chuchu & Dang, Tonghe & Hong, Jialin & Zhou, Tau, 2023. "CLT for approximating ergodic limit of SPDEs via a full discretization," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 1-41.
    2. di Nunno, Giulia & Ortiz–Latorre, Salvador & Petersson, Andreas, 2023. "SPDE bridges with observation noise and their spatial approximation," Stochastic Processes and their Applications, Elsevier, vol. 158(C), pages 170-207.

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    3. Wang, Xiaojie, 2020. "An efficient explicit full-discrete scheme for strong approximation of stochastic Allen–Cahn equation," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6271-6299.

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