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

E. Csáki, Miklós Csörgo, Antónia Földes, Pál Révész

Research output: Contribution to journalArticle

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 2009

Fingerprint

Brownian Sheet
Local Time
Brownian motion
Random walk
Strong Approximation
Wiener Process
Line
Local time
Brownian local time
Wiener process
Approximation

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Random walk local time approximated by a Brownian sheet combined with an independent Brownian motion. / Csáki, E.; Csörgo, Miklós; Földes, Antónia; Révész, Pál.

In: Annales de l'institut Henri Poincare (B) Probability and Statistics, Vol. 45, No. 2, 05.2009, p. 515-544.

Research output: Contribution to journalArticle

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