AUTHOR=Gao Han , Guo Rui , Jin Yang , Yan Litan TITLE=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 JOURNAL=Frontiers in Physics VOLUME=9 YEAR=2022 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2021.795210 DOI=10.3389/fphy.2021.795210 ISSN=2296-424X ABSTRACT=

Let S^H be a sub-fractional Brownian motion with index 12<H<1. In this paper, we consider the linear self-interacting diffusion driven by S^H, which is the solution to the equation

dXtH=dStH−θ(∫0tXtH−XsHds)dt+νdt,X0H=0,

where θ < 0 and ν∈R are two parameters. Such process X^H is called self-repelling and it is an analogue of the linear self-attracting diffusion [Cranston and Le Jan, Math. Ann. 303 (1995), 87–93]. Our main aim is to study the large time behaviors. We show the solution X^H diverges to infinity, as t tends to infinity, and obtain the speed at which the process X^H diverges to infinity as t tends to infinity.