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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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:157:y:2023:i:c:p:1-41
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DOI: 10.1016/j.spa.2022.11.015
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