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Large deviation principle for a class of SPDE with locally monotone coefficients

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Abstract

This work aims to prove the large deviation principle for a class of stochastic partial differential equations with locally monotone coefficients under the extended variational framework, which generalizes many previous works. Using stochastic control and the weak convergence approach, we prove the Laplace principle, which is equivalent to the large deviation principle in our framework. Instead of assuming compactness of the embedding in the corresponding Gelfand triple or finite dimensional approximation of the diffusion coefficient in some existing works, we only assume some temporal regularity in the diffusion coefficient.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11501147, 11501509, 11822106 and 11831014), the Natural Science Foundation of Jiangsu Province (Grant No. BK20160004), the QingLan Project and the Priority Academic Program Development of Jiangsu Higher Education Institutions. The authors are grateful to the anonymous referees for their careful reading of the manuscript and many helpful suggestions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, China

    Wei Liu & Chunyan Tao

  2. School of Science, Zhejiang University of Technology, Hangzhou, 310023, China

    Jiahui Zhu

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  1. Wei Liu
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  2. Chunyan Tao
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  3. Jiahui Zhu
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Correspondence to Wei Liu.

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Liu, W., Tao, C. & Zhu, J. Large deviation principle for a class of SPDE with locally monotone coefficients. Sci. China Math. 63, 1181–1202 (2020). https://doi.org/10.1007/s11425-018-9440-3

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