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CLT for approximating ergodic limit of SPDEs via a full discretization

Chuchu Chen, Tonghe Dang, Jialin Hong and Tau Zhou

Stochastic Processes and their Applications, 2023, vol. 157, issue C, 1-41

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.

Keywords: Central limit theorem; Stochastic partial differential equation; Full discretization; Poisson equation; Ergodic limit (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2022.11.015

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