Large Time Behavior on the Linear Self-Interacting Diffusion Driven by Sub-Fractional Brownian Motion With Hurst Index Large Than 0.5 I: Self-Repelling Case

Large Time Behavior on the Linear Self-Interacting Diffusion Driven by Sub-Fractional Brownian Motion With Hurst Index Large Than 0.5 I: Self-Repelling Case

Let SH be a sub-fractional Brownian motion with index 12<H<1. In this paper, we consider the linear self-interacting diffusion driven by SH, which is the solution to the equationdXtH=dStH−θ(∫0tXtH−XsHds)dt+νdt,X0H=0,where θ < 0 and ν∈R are two parameters. Such process XH is call...

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Bibliographic Details
Main Authors: Han Gao, Rui Guo, Yang Jin, Litan Yan
Format: Article
Language:English
Published: Frontiers Media S.A. 2022-01-01
Series:Frontiers in Physics
Subjects:
the self-repelling diffusion
asymptotic distribution
convergence
sub-fractional Brownian motion
stochastic integral
Online Access:https://www.frontiersin.org/articles/10.3389/fphy.2021.795210/full

Internet

https://www.frontiersin.org/articles/10.3389/fphy.2021.795210/full

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