Transient nearest neighbor random walk and Bessel process

Endre Csáki, Antónia Földes, Pál Révész

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We prove a strong invariance principle between a transient Bessel process and a certain nearest neighbor (NN) random walk that is constructed from the former by using stopping times. We show that their local times are close enough to share the same strong limit theorems. It is also shown that if the difference between the distributions of two NN random walks are small, then the walks themselves can be constructed in such a way that they are close enough. Finally, some consequences concerning strong limit theorems are discussed.

Original languageEnglish
Pages (from-to)992-1009
Number of pages18
JournalJournal of Theoretical Probability
Volume22
Issue number4
DOIs
Publication statusPublished - Oct 1 2009

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Keywords

  • Bessel process
  • Local time
  • Strong invariance principle
  • Strong theorems
  • Transient random walk

ASJC Scopus subject areas

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

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