Slow diffusion for a Brownian motion with random reflecting barriers

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:61

Article

关键词: regular variation;    reflected Brownian motion;    random media;    homogenization;    local time;   

DOI  :  10.1016/0304-4149(95)00073-9

来源: Elsevier

【 摘 要 】

Let beta be a positive number: we consider a particle performing a one-dimensional Brownian motion with drift -beta, diffusion coefficient 1, and a reflecting barrier at 0. We prove that the time R, needed by the particle to reach a random level X, has the same distribution tails as Gamma(alpha + 1)(1/alpha)e(2 beta X)/2 beta(2), provided that one of these tails is regularly varying with negative index -alpha. As a consequence, we discuss the asymptotic behaviour of a Brownian motion with random reflecting barriers, extending some results given by Solomon when X is exponential and alpha belongs to [1/2, 1].

【 授权许可】

Free