Mean-Field Backward Stochastic Differential Equations Driven by Fractional Brownian Motion  

作　　者：Yu Feng SHI Jia Qiang WEN Jie XIONG 

机构地区：[1]Institute for Financial Studies and School of Mathematics,Shandong University,Jinan 250100,P.R.China [2]Department of Mathematics,Southern University of Science and Technology,Shenzhen 518055,P.R.China [3]Department of Mat hematics and SUSTech International Center for Mathematics,Southern University of Science and Technology,Shenzhen 518055,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2021年第7期1156-1170,共15页数学学报（英文版）

基　　金：supported by the National Key R&D Program of China (Grant No. 2018YFA0703900);the National Natural Science Foundation of China (Grant Nos. 11871309 and 11371226);supported by China Postdoctoral Science Foundation (Grant No. 2019M660968);Southern University of Science and Technology Start up fund Y01286233;supported by Southern University of Science and Technology Start up fund Y01286120;the National Natural Science Foundation of China (Grants Nos. 61873325,11831010)

摘　　要：In this paper,we study a new class of equations called mean-field backward stochastic differential equations(BSDEs,for short)driven by fractional Brownian motion with Hurst parameter H>1/2.First,the existence and uniqueness of this class of BSDEs are obtained.Second,a comparison theorem of the solutions is established.Third,as an application,we connect this class of BSDEs with a nonlocal partial differential equation(PDE,for short),and derive a relationship between the fractional mean-field BSDEs and PDEs.

关 键 词：Mean-field backward stochastic differential equation fractional Brownian motion partial differential equation 

分 类 号：O211.63[理学—概率论与数理统计]