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

作者：Diel Roland^*

来源：Stochastic Processes and Their Applications, 2011, 121(10): 2303-2330.

DOI：10.1016/j.spa.2011.06.002

• Diffusion in Brownian environment
• Local time

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.

• 出版日期2011-10