Distribution dependent SDEs driven by fractional Brownian motions

Xiliang Fan, Xing Huang, Yongqiang Suo and Chenggui Yuan

Stochastic Processes and their Applications, 2022, vol. 151, issue C, 23-67

Abstract: In this paper we study a class of distribution dependent stochastic differential equations driven by fractional Brownian motions with Hurst parameter H∈(0,1/2)∪(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.

Keywords: Distribution dependent SDE; Fractional Brownian motion; Bismut type formula; Lions derivative; Wasserstein distance (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2022.05.007

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