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Zhan Shi

Publications and source records attributed to Zhan Shi.

132 records · Page 8Linked to original sources
arXiv2005

Moderate deviations for diffusions with Brownian potentials

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 tools in stochastic calculus, including Kotani's lemma and Lamperti's representation for exponential functionals. In particular, our result for quenched moderate deviations is in agreement with a recent theorem of Comets and Popov [Probab. Theory Related Fields 126 (2003) 571-609] who studied the corresponding problem for Sinai's random walk in random environment.

math.PR↗
arXiv2004

Frequently visited sets for random walks

We study the occupation measure of various sets for a symmetric transient random walk in $Z^d$ with finite variances. Let $μ^X_n(A)$ denote the occupation time of the set $A$ up to time $n$. It is shown that $\sup_{x\in Z^d}μ_n^X(x+A)/\log n$ tends to a finite limit as $n\to\infty$. The limit is expressed in terms of the largest eigenvalue of a matrix involving the Green's function of $X$ restricted to the set $A$. Some examples are discussed and the connection to similar results for Brownian motion is given.

math.PR↗
arXiv2000

Favourite sites of simple random walk

We survey the current status of the list of questions related to the favourite (or: most visited) sites of simple random walk on Z, raised by Pal Erdos and Pal Revesz in the early eighties.

math.PR↗
arXiv1998

An embedding for the Kesten-Spitzer random walk in random scenery

For one-dimensional simple random walk in a general i.i.d. scenery and its limiting process we construct a coupling with explicit rate of approximation extending a recent result for Gaussian sceneries due to Khoshnevisan and Lewis. Furthermore we explicity identify the constant in the law of iterated logarithm.

math.PR↗