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.
Publié le : 2009-05-15
Classification:
Local time,
random walk,
Brownian sheet,
strong approximation,
60J55,
60G50,
60F15,
60F17
@article{1241024679,
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 = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {45},
number = {1},
year = {2009},
pages = { 515-544},
language = {en},
url = {http://dml.mathdoc.fr/item/1241024679}
}
Csáki, Endre; Csörgő, Miklós; Földes, Antónia; Révész, Pál. Random walk local time approximated by a Brownian sheet combined with an independent Brownian motion. Ann. Inst. H. Poincaré Probab. Statist., Tome 45 (2009) no. 1, pp. 515-544. http://gdmltest.u-ga.fr/item/1241024679/