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Some Limit Theorems for Heights of Random Walks on a Spider |
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| Authors: | Endre Csáki Miklós Csörgő Antónia Földes Pál Révész |
| Institution: | 1.Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences,Budapest,Hungary;2.School of Mathematics and Statistics,Carleton University,Ottawa,Canada;3.Department of Mathematics,College of Staten Island, CUNY,Staten Island,USA;4.Institut für Statistik und Wahrscheinlichkeitstheorie,Technische Universit?t Wien,Vienna,Austria |
| Abstract: | A simple random walk is considered on a spider that is a collection of half lines (we call them legs) joined at the origin. We establish a strong approximation of this random walk by the so-called Brownian spider. Transition probabilities are studied, and for a fixed number of legs we investigate how high the walker and the Brownian motion can go on the legs in n steps. The heights on the legs are also investigated when the number of legs goes to infinity. |
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