Asymptotic behaviors for distribution dependent SDEs driven by fractional Brownian motions

2022/07/04 by Xiliang Fan, Ting Yu, Fan, Xiliang +3 · 2 citations
Economics, Econometrics and Finance · Mathematics · #60G22 #60H10 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2207.01525

openalex publication_date 2022/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study small-time asymptotic behaviors for a class of distribution dependent stochastic differential equations driven by fractional Brownian motions with Hurst parameter H∈(1/2,1) and magnitude \ep^H. By building up a variational framework and two weak convergence criteria in the factional Brownian motion setting, we establish the large and moderate deviation principles for this type equations. Besides, we also obtain the central limit theorem, in which the limit process solves a linear equation involving the Lions derivative of the drift coefficient.

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• McKean-Vlasov SPDEs driven by Poisson random measure: Well-posedness and large deviation principle

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