Strong limit theorems for a simple random walk on the 2-dimensional comb

Endre Csáki, Miklós Csörgő, Antónia Földes, Pál Révész

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

We study the path behaviour of a simple random walk on the 2-dimensional comb lattice C2 that is obtained from Z2 by removing all horizontal edges off the x-axis. In particular, we prove a strong approximation result for such a random walk which, in turn, enables us to establish strong limit theorems, like the joint Strassen type law of the iterated logarithm of its two components, as well as their marginal Hirsch type behaviour.

Original languageEnglish
Pages (from-to)2371-2390
Number of pages20
JournalElectronic Journal of Probability
Volume14
DOIs
Publication statusPublished - Jan 1 2009

Keywords

  • 2-dimensional Wiener
  • 2-dimensional comb
  • Random walk
  • Strong approximation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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