Csáki, Endre; Csörgő, Miklós; Földes, Antónia; Révész, Pál
Random walk local time approximated by a brownian sheet combined with an independent brownian motion
Annales de l'I.H.P. Probabilités et statistiques, Tome 45 (2009) no. 2 , p. 515-544
Zbl 1179.60051 | MR 2521412
doi : 10.1214/08-AIHP173
URL stable : http://www.numdam.org/item?id=AIHPB_2009__45_2_515_0

Classification:  60J55,  60G50,  60F15,  60F17
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.
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.

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