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

Zhen Wu and Ruimin Xu

Statistics & Probability Letters, 2019, vol. 145, issue C, 273-283

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.

Keywords: Mean-field BSDEs; McKean–Vlasov SDEs; McKean–Vlasov PDEs; Sobolev solution; Stochastic flow (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2018.10.001

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