Let $S_n$ be a random walk in $\bz^d$ and let $R_n$ be the range of $S_n$. We prove an almost sure invariance principle for $R_n$ when $d=3$ and a law of the iterated logarithm for $R_n$ when $d=2$.
Publié le : 2002-07-14
Classification:
Range of random walk,
law of the iterated logarithm,
law of the iterated logarithm,
intersection local time,
60J10,
60F15,
60G17
@article{1029867131,
author = {Bass, Richard F. and Kumagai, Takashi},
title = {Law of the iterated logarithm for the range of random walks in two and three dimensions},
journal = {Ann. Probab.},
volume = {30},
number = {1},
year = {2002},
pages = { 1369-1396},
language = {en},
url = {http://dml.mathdoc.fr/item/1029867131}
}
Bass, Richard F.; Kumagai, Takashi. Law of the iterated logarithm for the range of random walks in two and three dimensions. Ann. Probab., Tome 30 (2002) no. 1, pp. 1369-1396. http://gdmltest.u-ga.fr/item/1029867131/