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Asymptotic behaviors for distribution dependent SDEs driven by fractional Brownian motions

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  • Fan, Xiliang
  • Yu, Ting
  • Yuan, Chenggui

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.

Suggested Citation

  • Fan, Xiliang & Yu, Ting & Yuan, Chenggui, 2023. "Asymptotic behaviors for distribution dependent SDEs driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 383-415.
    • Handle: RePEc:eee:spapps:v:164:y:2023:i:c:p:383-415
    DOI: 10.1016/j.spa.2023.07.015
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    References listed on IDEAS

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    1. Adams, Daniel & dos Reis, Gonçalo & Ravaille, Romain & Salkeld, William & Tugaut, Julian, 2022. "Large Deviations and Exit-times for reflected McKean–Vlasov equations with self-stabilising terms and superlinear drifts," Stochastic Processes and their Applications, Elsevier, vol. 146(C), pages 264-310.
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    8. Fan, Xiliang & Huang, Xing & Suo, Yongqiang & Yuan, Chenggui, 2022. "Distribution dependent SDEs driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 151(C), pages 23-67.
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