Distribution dependent SDEs driven by fractional Brownian motions

Xiliang Fan; Xing Huang; Yongqiang Suo; Chenggui Yuan

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arXiv · 2105.14341

Distribution dependent SDEs driven by fractional Brownian motions

Xiliang Fan·Xing Huang·Yongqiang Suo·Chenggui Yuan

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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.

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Xiliang Fan, Xing Huang, Yongqiang Suo, Chenggui Yuan. 2021-05-29. Distribution dependent SDEs driven by fractional Brownian motions. https://arxiv.org/abs/2105.14341

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