Random walk local time approximated by a Brownian sheet combined with an independent Brownian motion

Endre Csáki, Miklós Csörgo, Antónia Földes, Pál Révész

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3 Citations (Scopus)

Abstract

Let ξ(k,n) be the local time of a simple symmetric random walk on the line. We give a strong approximation of the centered local time process ξ(k,n)-ξ(0,n) in terms of a Brownian sheet and an independent Wiener process (Brownian motion), time changed by an independent Brownian local time. Some related results and consequences are also established.

Original languageEnglish
Pages (from-to)515-544
Number of pages30
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume45
Issue number2
DOIs
Publication statusPublished - May 1 2009

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Keywords

  • Brownian sheet
  • Local time
  • Random walk
  • Strong approximation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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