Open AccessGeneralized Mean-Field Fractional BSDEs With Non-Lipschitz Coefficients
Author(s) -
Qun Shi
Publication year - 2021
Publication title -
international journal of statistics and probability
Language(s) - English
Resource type - Journals
eISSN - 1927-7040
pISSN - 1927-7032
DOI - 10.5539/ijsp.v10n3p77
Subject(s) - mathematics , lipschitz continuity , stochastic differential equation , mean field theory , brownian motion , type (biology) , fractional brownian motion , geometric brownian motion , comparison theorem , mathematical analysis , field (mathematics) , pure mathematics , diffusion process , statistics , computer science , ecology , knowledge management , physics , innovation diffusion , quantum mechanics , biology
In this paper we consider one dimensional generalized mean-field backward stochastic differential equations (BSDEs) driven by fractional Brownian motion, i.e., the generators of our mean-field FBSDEs depend not only on the solution but also on the law of the solution. We first give a totally new comparison theorem for such type of BSDEs under Lipschitz condition. Furthermore, we study the existence of the solution of such mean-field FBSDEs when the coefficients are only continuous and with a linear growth.