Some Limit Theorems for Heights of Random Walks on a Spider

Endre Csáki (), Miklós Csörgő (), Antónia Földes () and Pál Révész ()
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Endre Csáki: Hungarian Academy of Sciences
Miklós Csörgő: Carleton University
Antónia Földes: College of Staten Island, CUNY
Pál Révész: Technische Universität Wien

Journal of Theoretical Probability, 2016, vol. 29, issue 4, 1685-1709

Abstract: 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.

Keywords: Random walk on a spider; Brownian spider; Transition probabilities; Strong approximations; Laws of the iterated logarithm; Brownian and random walk heights on spider; Primary: 60F05; 60F15; 60G50; Secondary: 60J65; 60J10 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10959-015-0626-8

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