Author:
Yan Litan,Wu Xue,Xia Xiaoyu
Abstract
Let BH={BtH,t≥0} be a fractional Brownian motion with Hurst index 12≤H<1. In this paper, we consider the linear self-attracting diffusion: dXtH=dBtH+σXtHdt−θ∫0tXsH−XuHdsdt+νdt with X0H=0, where θ>0 and σ,ν∈R are three parameters. The process is an analogue of the 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 that the solution t−σθHXtH−X∞H converges in distribution to a normal random variable, as t tends to infinity, and obtain two strong laws of large numbers associated with the solution XH.
Funder
National Natural Science Foundation of China
Subject
Statistics and Probability,Statistical and Nonlinear Physics,Analysis
Cited by
1 articles.
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