JOURNAL ARTICLE

Rate of convergence for the Smoluchowski–Kramers approximation for distribution-dependent SDEs driven by fractional Brownian motions.

  • Published In: Stochastics & Dynamics, 2024, v. 24, n. 1. P. 1 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Liu, Wei; Pei, Bin; Yu, Qian 3 of 3

Abstract

In this paper, we study the rate in the Smoluchowski–Kramers approximation for the solution of the following distribution-dependent SDE driven by fractional Brownian motion X t = X 0 + ∫ 0 t b (s , X s , ℒ X s ) d s + ∫ 0 t σ (s , ℒ X s ) B s H , where ℒ X t denotes the law of X t , { B t H , t ∈ [ 0 , T ] } is a d -dimensional fractional Brownian motion with Hurst parameter H ∈ (1 / 2 , 1). Based on the techniques of multiple integrals and Malliavin calculus, we provide an explicit bound on total variation distance for the rate of convergence. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Stochastics & Dynamics. 2024/02, Vol. 24, Issue 1, p1
  • Document Type:Article
  • Subject Area:History
  • Publication Date:2024
  • ISSN:0219-4937
  • DOI:10.1142/S0219493724500023
  • Accession Number:177204749
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