Frequently visited sets for random walks

Endre Csáki, Antónia Földes, Pál Révész, Jay Rosen, Zhan Shi

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We study the occupation measure of various sets for a symmetric transient random walk in Zd with finite variances. Let μnX (A) denote the occupation time of the set A up to time n. It is shown that supx∈Zd μn X (x + A)/log n tends to a finite limit as n → ∞. 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.

Original languageEnglish
Pages (from-to)1503-1517
Number of pages15
JournalStochastic Processes and their Applications
Volume115
Issue number9
DOIs
Publication statusPublished - Sep 1 2005

Keywords

  • Occupation measure
  • Random walk
  • Strong theorems

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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