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Frequently visited sets for random walks

Author

Listed:
  • Csáki, Endre
  • Földes, Antónia
  • Révész, Pál
  • Rosen, Jay
  • Shi, Zhan

Abstract

We study the occupation measure of various sets for a symmetric transient random walk in Zd with finite variances. Let denote the occupation time of the set A up to time n. It is shown that tends to a finite limit as n-->[infinity]. 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.

Suggested Citation

  • Csáki, Endre & Földes, Antónia & Révész, Pál & Rosen, Jay & Shi, Zhan, 2005. "Frequently visited sets for random walks," Stochastic Processes and their Applications, Elsevier, vol. 115(9), pages 1503-1517, September.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:9:p:1503-1517
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    Cited by:

    1. Endre Csáki & Antónia Földes & Pál Révész, 2007. "On the Behavior of Random Walk Around Heavy Points," Journal of Theoretical Probability, Springer, vol. 20(4), pages 1041-1057, December.
    2. Csáki, Endre & Földes, Antónia & Révész, Pál, 2006. "Heavy points of a d-dimensional simple random walk," Statistics & Probability Letters, Elsevier, vol. 76(1), pages 45-57, January.

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