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, pp. 515-544.

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.

DOI : 10.1214/08-AIHP173
Classification : 60J55, 60G50, 60F15, 60F17
Mots-clés : local time, random walk, brownian sheet, strong approximation 
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     author = {Cs\'aki, Endre and Cs\"org\H{o}, Mikl\'os and F\"oldes, Ant\'onia and R\'ev\'esz, P\'al},
     title = {Random walk local time approximated by a brownian sheet combined with an independent brownian motion},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {515--544},
     publisher = {Gauthier-Villars},
     volume = {45},
     number = {2},
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     mrnumber = {2521412},
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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, pp. 515-544. doi : 10.1214/08-AIHP173. http://archive.numdam.org/articles/10.1214/08-AIHP173/

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