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CLT for approximating ergodic limit of SPDEs via a full discretization

Author

Listed:
  • Chen, Chuchu
  • Dang, Tonghe
  • Hong, Jialin
  • Zhou, Tau

Abstract

In order to characterize quantitatively the fluctuations between the ergodic limit and the time-averaging estimator, we establish a central limit theorem for a full discretization of the parabolic SPDE, which shows that the normalized time-averaging estimator converges weakly to a normal distribution as the time stepsize tends to 0. A key ingredient in the proof is to extract an appropriate martingale difference series sum from the normalized time-averaging estimator via the Poisson equation, so that convergences of such a sum and the remainder are well balanced.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:157:y:2023:i:c:p:1-41
    DOI: 10.1016/j.spa.2022.11.015
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    References listed on IDEAS

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    1. 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.
    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.
    3. Komorowski, Tomasz & Walczuk, Anna, 2012. "Central limit theorem for Markov processes with spectral gap in the Wasserstein metric," Stochastic Processes and their Applications, Elsevier, vol. 122(5), pages 2155-2184.
    Full references (including those not matched with items on IDEAS)

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