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Large Deviations for Quasilinear Parabolic Stochastic Partial Differential Equations

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Abstract

In this paper, we establish the Freidlin-Wentzell’s large deviations for quasilinear parabolic stochastic partial differential equations with multiplicative noise, which are neither monotone nor locally monotone. The proof is based on the weak convergence approach.

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Acknowledgements

The authors are grateful to the anonymous referees for comments and suggestions. This work is partly supported by National Natural Science Foundation of China (No.11371041, 11671372, 11431014, 11401557, 11801032). Key Laboratory of Random Complex Structures and Data Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences (No. 2008DP173182). China Postdoctoral Science Foundation funded project (No. 2018M641204).

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Authors and Affiliations

  1. RCSDS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Zhao Dong

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China

    Zhao Dong

  3. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China

    Rangrang Zhang

  4. School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK

    Tusheng Zhang

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  1. Zhao Dong
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  2. Rangrang Zhang
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  3. Tusheng Zhang
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Correspondence to Rangrang Zhang.

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Dong, Z., Zhang, R. & Zhang, T. Large Deviations for Quasilinear Parabolic Stochastic Partial Differential Equations. Potential Anal 53, 183–202 (2020). https://doi.org/10.1007/s11118-019-09763-1

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  • DOI: https://doi.org/10.1007/s11118-019-09763-1

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