On the local time of random walk on the 2-dimensional comb |
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| Authors: | Endre Csáki Miklós Csörg? |
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| Institution: | a Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, P.O.B. 127, H-1364, Hungaryb School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, Canada K1S 5B6c Department of Mathematics, College of Staten Island, CUNY, 2800 Victory Blvd., Staten Island, NY 10314, USAd Institut für Statistik und Wahrscheinlichkeitstheorie, Technische Universität Wien, Wiedner Hauptstrasse 8-10/107 A-1040 Vienna, Austria |
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| Abstract: | We study the path behaviour of general random walks, and that of their local times, on the 2-dimensional comb lattice C2 that is obtained from Z2 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. |
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| Keywords: | primary 60F17 60G50 60J65 secondary 60F15 60J10 |
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