Distribution dependent SDEs driven by fractional Brownian motions

2021/05/29 by Fan, Xiliang, Huang, Xing, Suo, Yongqiang +1 · 2 citations
#60G22 #60H10 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2105.14341

Abstract

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.

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• Euler-Maruyama method for distribution dependent stochastic differential equation driven by multiplicative fractional Brownian motion
• Uniform measure attractors of the distribution-dependent 2D stochastic Navier-Stokes equations driven by nonlinear noise

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