Frequently visited sets for random walks
نویسندگان
چکیده
We study the occupation measure of various sets for a symmetric transient random walk in Z with finite variances. Let mn ðAÞ denote the occupation time of the set A up to time n. It is shown that supx2Zd m X n ðx þ AÞ= log n tends to a finite limit as n ! 1. The limit is expressed in terms of the largest eigenvalue of a matrix involving the Green function of X restricted to the set A. Some examples are discussed and the connection to similar results for Brownian motion is given. r 2005 Elsevier B.V. All rights reserved. MSC: primary 60G50; secondary 60F15; secondary 60J55
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تاریخ انتشار 2004