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Asymptotic Behaviors of Small Perturbation for Multivalued Mckean–Vlasov Stochastic Differential Equations

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Abstract

In this paper we study the asymptotic behaviors of small perturbation for a class of multivalued McKean–Vlasov stochastic differential equations. By using the weak convergence approach, we establish the large and moderate deviation principles. We also obtain the central limit theorem, in which the limit process is a solution to some multivalued McKean–Vlasov stochastic differential equation involving the Lions derivative in the drift coefficient.

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Acknowledgements

Four authors are grateful to two referees since their suggestions and comments allowed them to improve the results and the presentation of this paper.

Funding

This work is supported by NSF of China (No.12071071, 12071361, 12131019).

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Authors and Affiliations

  1. School of Mathematics, Southeast University, Nanjing, 211189, Jiangsu, China

    Kun Fang & Huijie Qiao

  2. School of Mathematics and Statistics, Wuhan University Wuhan, Hubei, 430072, China

    Wei Liu & Fengwu Zhu

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  1. Kun Fang
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  2. Wei Liu
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  3. Huijie Qiao
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  4. Fengwu Zhu
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Contributions

Four authors contributed to the study conception and design. The first draft of the manuscript was written by KF and four authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Huijie Qiao.

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Four authors have no relevant financial or non-financial interests to disclose.

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Fang, K., Liu, W., Qiao, H. et al. Asymptotic Behaviors of Small Perturbation for Multivalued Mckean–Vlasov Stochastic Differential Equations. Appl Math Optim 88, 22 (2023). https://doi.org/10.1007/s00245-023-10004-6

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