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On the local time of random walk on the 2-dimensional comb

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  • Csáki, Endre
  • Csörgo, Miklós
  • Földes, Antónia
  • Révész, Pál

Abstract

We study the path behaviour of general random walks, and that of their local times, on the 2-dimensional comb lattice that is obtained from by removing all horizontal edges off the x-axis. We prove strong approximation results for such random walks and also for their local times. Concentrating mainly on the latter, we establish strong and weak limit theorems, including Strassen-type laws of the iterated logarithm, Hirsch-type laws, and weak convergence results in terms of functional convergence in distribution.

Suggested Citation

  • Csáki, Endre & Csörgo, Miklós & Földes, Antónia & Révész, Pál, 2011. "On the local time of random walk on the 2-dimensional comb," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1290-1314, June.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:6:p:1290-1314
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    References listed on IDEAS

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