Almost sure asymptotics for the maximum local time in Brownian environment

Details Almost sure asymptotics for the maximum local time in Brownian environment Almost sure asymptotics for the maximum local time in Brownian environment

2010-03-02

arxiv.org/abs/1003.0661v2

Mathematics

Probability

Scientific paper

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)).

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