Some Limit Theorems for Heights of Random Walks on a Spider

Endre Csáki, Miklós Csörgő, Antónia Földes, Pál Révész

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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.

Original languageEnglish
Pages (from-to)1685-1709
Number of pages25
JournalJournal of Theoretical Probability
Volume29
Issue number4
DOIs
Publication statusPublished - Dec 1 2016

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Keywords

  • Brownian and random walk heights on spider
  • Brownian spider
  • Laws of the iterated logarithm
  • Random walk on a spider
  • Strong approximations
  • Transition probabilities

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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