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Probabilistic interpretation for Sobolev solutions of McKean–Vlasov partial differential equations

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  • Wu, Zhen
  • Xu, Ruimin

Abstract

In this paper, we give a probabilistic interpretation of Sobolev solutions to parabolic semilinear McKean–Vlasov partial differential equations (PDEs for short) in terms of mean-field backward stochastic differential equations (BSDEs for short). This probabilistic interpretation can be viewed as a generalization of the Feynman–Kac formula. The method is based on the stochastic flow technique which is different from classical stochastic differential equations (SDEs for short) due to the influence of mean-field term in McKean–Vlasov SDEs.

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  • Wu, Zhen & Xu, Ruimin, 2019. "Probabilistic interpretation for Sobolev solutions of McKean–Vlasov partial differential equations," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 273-283.
    • Handle: RePEc:eee:stapro:v:145:y:2019:i:c:p:273-283
    DOI: 10.1016/j.spl.2018.10.001
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    References listed on IDEAS

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    1. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
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