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

被引：1

作者：

Wu, Zhen ^{[1
]}

Xu, Ruimin ^{[2
]}

机构：

[1] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China

[2] Qilu Univ Technol, Shandong Acad Sci, Sch Math & Stat, Jinan 250353, Shandong, Peoples R China

来源：

STATISTICS & PROBABILITY LETTERS | 2019年 / 145卷

关键词：

Mean-field BSDEs; McKean-Vlasov SDEs; McKean-Vlasov PDEs; Sobolev solution; Stochastic flow; MEAN-FIELD GAMES; WEAK SOLUTIONS; LEVY PROCESSES;

D O I：

10.1016/j.spl.2018.10.001

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：273 / 283

页数：11

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