摘要
Let B^(H) be a fractional Brownian motion with Hurst index 1/2≤H<1.In this paper,we consider the equation(called the Ornstein-Uhlenbeck process with a linear self-repelling drift)dX_(t)^(H)=dB_(t)^(H)+σ X_(t)^(H)dt+vdt-θ(∫_(0)^(t)(X_(t)^(H)-X_(s)^(H))ds)dt,whereθ<0,σ,v∈ℝ.The process is an analogue of self-attracting diffusion(Cranston,Le Jan.Math Ann,1995,303:87–93).Our main aim is to study the large time behaviors of the process.We show that 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.
作者
夏晓宇
闫理坦
杨晴
Xiaoyu XIA;Litan YAN;Qing YANG(College of Information Science and Technology,Donghua University,Shanghai,201620,China;Department of Statistics,College of Science,Donghua University,Shanghai,201620,China)
基金
supported by the NSFC(11971101).
