Open Access
Translator Disclaimer
May 2009 Random walk local time approximated by a Brownian sheet combined with an independent Brownian motion
Endre Csáki, Miklós Csörgő, Antónia Földes, Pál Révész
Ann. Inst. H. Poincaré Probab. Statist. 45(2): 515-544 (May 2009). DOI: 10.1214/08-AIHP173

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.

Soit ξ(k, n) le temps local d’une marche aléatoire simple et symétrique sur la droite réelle. Nous donnons une approximation forte de la différence des temps locaux ξ(k, n)−ξ(0, n) en termes d’un drap Brownien et d’un processus de Wiener indépendant, évalué au temps local d’un mouvement Brownien indépendant. Des applications de ce résultat sont établies.

Citation

Download Citation

Endre Csáki. Miklós Csörgő. Antónia Földes. Pál Révész. "Random walk local time approximated by a Brownian sheet combined with an independent Brownian motion." Ann. Inst. H. Poincaré Probab. Statist. 45 (2) 515 - 544, May 2009. https://doi.org/10.1214/08-AIHP173

Information

Published: May 2009
First available in Project Euclid: 29 April 2009

zbMATH: 1179.60051
MathSciNet: MR2521412
Digital Object Identifier: 10.1214/08-AIHP173

Subjects:
Primary: 60G50 , 60J55
Secondary: 60F15 , 60F17

Keywords: Brownian sheet , Local time , Random walk , strong approximation

Rights: Copyright © 2009 Institut Henri Poincaré

JOURNAL ARTICLE
30 PAGES


SHARE
Vol.45 • No. 2 • May 2009
Back to Top