Distribution dependent SDEs driven by fractional Brownian motions

TL;DR

This paper investigates distribution dependent stochastic differential equations driven by fractional Brownian motions with Hurst parameter H in (1/2,1), establishing well-posedness, Bismut formulas, and derivative estimates.

Contribution

It introduces the first well-posedness results and Bismut formulas for such equations driven by fractional Brownian motions, extending stochastic analysis tools.

Findings

Proved well-posedness of distribution dependent SDEs driven by fractional Brownian motions.

Derived Bismut formulas for Lions derivatives in this context.

Provided estimates for Lions derivatives and total variation distances.

Abstract

In this paper we study a class of distribution dependent stochastic differential equations driven by fractional Brownian motions with Hurst parameter H\in(1/2,1). We prove the well-posedness of this type equations, and then establish a general result on the Bismut formula for the Lions derivative by using Malliavin calculus. 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.