Semilinear stochastic partial differential equations: Central limit theorem and moderate deviations

In this paper, we establish a central limit theorem (CLT) and the moderate deviation principles (MDP) for a class of semilinear stochastic partial differential equations driven by multiplicative noise on a bounded domain. The main results can be applied to stochastic partial differential equations o...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2021-05, Vol.44 (8), p.6808-6838
Main Authors: Xiong, Jie, Zhang, Rangrang
Format: Article
Language:English
Subjects:
Burgers equation
Central limit theorem
Deviation
Garsia lemma
Mathematical analysis
moderate deviation principles
Partial differential equations
semilinear partial differential equations
space‐time white noise
Theorems
White noise
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Summary:In this paper, we establish a central limit theorem (CLT) and the moderate deviation principles (MDP) for a class of semilinear stochastic partial differential equations driven by multiplicative noise on a bounded domain. The main results can be applied to stochastic partial differential equations of various types such as the stochastic Burgers equation and the reaction‐diffusion equations perturbed by space‐time white noise. The Garsia lemma is crucial to our results.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.7224