Frequently visited sets for random walks

E. Csáki, Antónia Földes, Pál Révész, Jay Rosen, Zhan Shi

Research output: Contribution to journalArticle

5 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 2005

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Brownian movement
Green's function
Random walk
Occupation Measure
Occupation Time
Largest Eigenvalue
Brownian motion
Tend
Denote
Eigenvalues

Keywords

  • Occupation measure
  • Random walk
  • Strong theorems

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Mathematics(all)
  • Statistics and Probability
  • Modelling and Simulation

Cite this

Frequently visited sets for random walks. / Csáki, E.; Földes, Antónia; Révész, Pál; Rosen, Jay; Shi, Zhan.

In: Stochastic Processes and their Applications, Vol. 115, No. 9, 09.2005, p. 1503-1517.

Research output: Contribution to journalArticle

Csáki, E, Földes, A, Révész, P, Rosen, J & Shi, Z 2005, 'Frequently visited sets for random walks', Stochastic Processes and their Applications, vol. 115, no. 9, pp. 1503-1517. https://doi.org/10.1016/j.spa.2005.04.003
Csáki, E. ; Földes, Antónia ; Révész, Pál ; Rosen, Jay ; Shi, Zhan. / Frequently visited sets for random walks. In: Stochastic Processes and their Applications. 2005 ; Vol. 115, No. 9. pp. 1503-1517.
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