Zhan Shi

activity

20032005

most citedModerate deviations for diffusions with Brownian potentials

20 citations · 39 across the 6 of their papers we have counts for

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Showing math.PRShow all

5 papers · 1 filter

math.PR2005★ 1 cited

Valleys and the maximum local time for random walk in random environment

Amir Dembo, Nina Gantert, Yuval Peres +1

Let $ξ (n, x)$ be the local time at $x$ for a recurrent one-dimensional random walk in random environment after $n$ steps, and consider the maximum $ξ^{*} (n) = max_{x} ξ (n, x)$ . It is k…

math.PR2005★ 20 cited

Moderate deviations for diffusions with Brownian potentials

Yueyun Hu, Zhan Shi

We present precise moderate deviation probabilities, in both quenched and annealed settings, for a recurrent diffusion process with a Brownian potential. Our method relies on fine…

math.PR2004★ 1 cited

Frequently visited sets for random walks

Endre Csáki, Antónia Földes, Pál Révész +2

We study the occupation measure of various sets for a symmetric transient random walk in $Z^{d}$ with finite variances. Let $μ_{n}^{X} (A)$ denote the occupation time of the set $A$ up to…

math.PR2004

An Extreme-Value Analysis of the LIL for Brownian Motion

Davar Khoshnevisan, David A. Levin, Zhan Shi

We present an extreme-value analysis of the classical law of the iterated logarithm (LIL) for Brownian motion. Our result can be viewed as a new improvement to the LIL.

math.PR2004

Annealed deviations of random walk in random scenery

Nina Gantert, Wolfgang König, Zhan Shi

Let $(Z_{n})_{n \in N}$ be a $d$ -dimensional {\it random walk in random scenery}, i.e., $Z_{n} = \sum_{k = 0}^{n - 1} Y (S_{k})$ with $(S_{k})_{k \in N_{0}}$ a random walk in $Z^{d}$ and $(Y(z))_{z\in\…