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Central Limit Theorem and Moderate Deviations for a Class of Semilinear Stochastic Partial Differential Equations

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Abstract

In this paper we prove a central limit theorem and a moderate deviation principle for a class of semilinear stochastic partial differential equations, which contain the stochastic Burgers’ equation and the stochastic reaction-diffusion equation. The weak convergence method plays an important role.

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Acknowledgements

We would like to express our appreciation for R. Belfadli, L. Boulanba and M. Mellouk. They told us about their work on the stochastic Burgers’ equation and pointed out a mistake in our paper.

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Authors and Affiliations

  1. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, 430073, China

    Shulan Hu

  2. School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai, 201620, China

    Ruinan Li

  3. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China

    Xinyu Wang

Authors
  1. Shulan Hu
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  2. Ruinan Li
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  3. Xinyu Wang
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Corresponding author

Correspondence to Xinyu Wang.

Additional information

The research of HU was supported by NSFF (17BTJ034). The research of WANG was supported by NSFC (11871382, 11771161).

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Hu, S., Li, R. & Wang, X. Central Limit Theorem and Moderate Deviations for a Class of Semilinear Stochastic Partial Differential Equations. Acta Math Sci 40, 1477–1494 (2020). https://doi.org/10.1007/s10473-020-0518-6

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  • DOI: https://doi.org/10.1007/s10473-020-0518-6

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