线性分数自排斥扩散的收敛性

Convergence of the linear fractional self-repelling diffusion

考察了由分数布朗运动驱动的线性自排斥扩散过程的收敛性:Xt^H=Bt^H+a∫0t∫0s(Xs^H-Xu^H)duds+vt,X0^H=0,其中BH是Hurst指数为H>1/2的分数布朗运动,a>0,v∈R是已知的常数。证明了其解在特定的收敛速度下以概率1与L^2(Ω)收敛于一个随机变量。

In this paper,we investigated the asymptotic behavior of the linear self-repelling diffusion driven by fractional Brownian motion. Xt^H=Bt^H+a∫0t∫0s(Xs^H-Xu^H)duds+vt,X0^H=0,where BH is fractional Brownian motion with Hurst index H>1/2,a>0,v∈R are two constants. te^1/2at^2 Xt^H is proved to converge to a normal random variable as t(t→+∞) almost surely and in L2(Ω).