Almost sure asymptotics for the maximum local time in Brownian environment
Probability
2015-03-13 v2
Abstract
We study the asymptotic behaviour of the maximum local time L*(t) of the Brox's process, the diffusion in Brownian environment. Shi proved that the maximum speed of L*(t) is surprisingly, at least t log(log(log t)) whereas in the discrete case it is t. We show here that t log(log(log t)) is the proper rate and we prove that for the minimum speed the rate is the same as in the discrete case namely t/log(log(log t)).
Cite
@article{arxiv.1003.0661,
title = {Almost sure asymptotics for the maximum local time in Brownian environment},
author = {Roland Diel},
journal= {arXiv preprint arXiv:1003.0661},
year = {2015}
}