Distribution dependent SDEs driven by fractional Brownian motions

Work of Xing Huang

(Joint with Xiliang Fan, Yongqiang Suo,

Chenggui Yuan)

In this paper we study a class of distribution dependent stochastic differential equations driven by fractional Brownian motions. We prove the well-posedness of this type equations with additive noise, where the coefficient before the noise is allowed to be distribution dependent if the Hurst parameter is bigger than 1/2. We also establish a general result on the Bismut formula for the Lions derivative by using Malliavin calculus in the case that the coefficient before the noise is distribution free. As applications, we provide the Bismut formulas of this kind for both non-degenerate and degenerate cases, and obtain the estimates of the Lions derivative and the total variation distance between the laws of two solutions.

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

https://doi.org/10.1016/j.spa.2022.05.007

Research Highlight 26-Apr.3]