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

Endre Csáki, Miklós Csörgo, Antónia Földes and Pál Révész

Stochastic Processes and their Applications, 2011, vol. 121, issue 6, 1290-1314

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.

Keywords: Random; walk; 2-dimensional; comb; Strong; approximation; 2-dimensional; Wiener; process; Local; time; Laws; of; the; iterated; logarithm; Iterated; Brownian; motion (search for similar items in EconPapers)
Date: 2011
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