Localization of favorite points for diffusion in random environment
Abstract
For a diffusion Xt in a one-dimensional Wiener medium W, it is known that there is a certain process bx(W) that depends only on the environment W, so that Xt-blogt(W) converges in distribution as t goes to infinity. We prove that, modulo a relatively small time change, the process bx(W):x>0is followed closely by the process FX(ex): x>0, with FX(t) denoting the point with the most local time for the diffusion at time t.
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