Distribution dependent SDEs driven by fractional Brownian motions

By Xiliang Fan, Xing Huang, Yongqiang Suo, Chenggui Yuan. Stochastic Processes and their Applications, 2021

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In this paper we study a class of distribution dependent stochastic differential equations driven by fractional Brownian motions with Hurst parameter H ∈ (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. AMS Subject Classification: 60H10, 60G22

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/130ee4eb632a266b7484765aa1ead1f76dca8c46