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Large Deviation Principle for McKean–Vlasov Quasilinear Stochastic Evolution Equations

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Abstract

This paper is devoted to investigating the Freidlin–Wentzell’s large deviation principle for a class of McKean–Vlasov quasilinear SPDEs perturbed by small multiplicative noise. We adopt the variational framework and the modified weak convergence criteria to prove the Laplace principle for McKean–Vlasov type SPDEs, which is equivalent to the large deviation principle. Moreover, we do not assume any compactness condition of embedding in the Gelfand triple to handle both the cases of bounded and unbounded domains in applications. The main results can be applied to various McKean–Vlasov type SPDEs such as distribution dependent stochastic porous media type equations and stochastic p-Laplace type equations.

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Acknowledgements

The authors would like to thank the referees for their very constructive suggestions and valuable comments. The research of S. Li is supported by NSFC (No. 12001247), NSF of Jiangsu Province (No. BK20201019), NSF of Jiangsu Higher Education Institutions of China (No. 20KJB110015) and the Foundation of Jiangsu Normal University (No. 19XSRX023). The research of W. Liu is supported by NSFC (No. 11822106, 11831014, 12090011) and the PAPD of Jiangsu Higher Education Institutions.

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Authors and Affiliations

  1. Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China

    Wei Hong

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

    Shihu Li & Wei Liu

  3. Research Institute of Mathematical Sciences, Jiangsu Normal University, Xuzhou, 221116, China

    Wei Liu

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  1. Wei Hong
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Hong, W., Li, S. & Liu, W. Large Deviation Principle for McKean–Vlasov Quasilinear Stochastic Evolution Equations. Appl Math Optim 84 (Suppl 1), 1119–1147 (2021). https://doi.org/10.1007/s00245-021-09796-2

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