Asymptotic behaviors for distribution dependent SDEs driven by fractional Brownian motions

Xiliang Fan, Ting Yu and Chenggui Yuan

Stochastic Processes and their Applications, 2023, vol. 164, issue C, 383-415

Abstract: In this paper, we study small-noise 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 ϵH. 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 these types of 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.

Keywords: Distribution dependent SDE; Fractional Brownian motion; Large deviation principle; Moderate deviation principle; Central limit theorem (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2023.07.015

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