AUTHOR=Guo Rui , Gao Han , Jin Yang , Yan Litan TITLE=Large Time Behavior on the Linear Self-Interacting Diffusion Driven by Sub-Fractional Brownian Motion II: Self-Attracting Case JOURNAL=Frontiers in Physics VOLUME=9 YEAR=2022 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2021.791858 DOI=10.3389/fphy.2021.791858 ISSN=2296-424X ABSTRACT=

In this study, as a continuation to the studies of the self-interaction diffusion driven by subfractional Brownian motion S^H, we analyze the asymptotic behavior of the linear self-attracting diffusion:dXtH=dStH−θ∫0t(XtH−XsH)dsdt+νdt,X0H=0,

where θ > 0 and ν∈R are two parameters. When θ < 0, the solution of this equation is called self-repelling. Our main aim is to show the solution X^H converges to a normal random variable X∞H with mean zero as t tends to infinity and obtain the speed at which the process X^H converges to X∞H as t tends to infinity.