Almost sure asymptotics for the local time of a diffusion in Brownian environment

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:121

Article

Diel, Roland

关键词: Diffusion in Brownian environment;    Local time;   

DOI  :  10.1016/j.spa.2011.06.002

来源: Elsevier

【 摘 要 】

Here, we study the asymptotic behavior of the maximum local time L*(t) of the diffusion in Brownian environment. Shi (1998) [17] proved that, surprisingly, the maximum speed of L*(t) is at least t log(log(log t)); whereas in the discrete case, it is t. We show that t log(log(log t)) is the proper rate and that for the minimum speed the rate is the same as in the discrete case (see Dembo et al. (2007) [6]) namely t/log(log(log t)). We also prove a localization result: almost surely for large time, the diffusion has spent almost all the time in the neighborhood of four points which only depend on the environment. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free