首页|THE LONG TIME BEHAVIOR OF THE FRACTIONAL ORNSTEIN-UHLENBECK PROCESS WITH LINEAR SELF-REPELLING DRIFT
THE LONG TIME BEHAVIOR OF THE FRACTIONAL ORNSTEIN-UHLENBECK PROCESS WITH LINEAR SELF-REPELLING DRIFT
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Let BH 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)dXHt=dBHt+σXHtdt+vdt-θ(∫t0(XHt-XHs)ds)dt,where θ＜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 XH diverges to infinity as t tends to infinity,and obtain the speed at which the process XH diverges to infinity as t tends to infinity.
fractional Brownian motionstochastic difference equationsrate of conver-genceasymptotic
夏晓宇、闫理坦、杨晴
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College of Information Science and Technology,Donghua University,Shanghai 201620,China
Department of Statistics,College of Science,Donghua University,Shanghai 201620,China
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