Open Access
Translator Disclaimer
July 2002 Law of the iterated logarithm for the range of random walks in two and three dimensions
Richard F. Bass, Takashi Kumagai
Ann. Probab. 30(3): 1369-1396 (July 2002). DOI: 10.1214/aop/1029867131

Abstract

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 $d=2$.

Citation

Download Citation

Richard F. Bass. Takashi Kumagai. "Law of the iterated logarithm for the range of random walks in two and three dimensions." Ann. Probab. 30 (3) 1369 - 1396, July 2002. https://doi.org/10.1214/aop/1029867131

Information

Published: July 2002
First available in Project Euclid: 20 August 2002

zbMATH: 1031.60031
MathSciNet: MR1920111
Digital Object Identifier: 10.1214/aop/1029867131

Subjects:
Primary: 60J10
Secondary: 60F15 , 60G17

Keywords: Intersection local time , Law of the iterated logarithm , Law of the iterated logarithm , Range of random walk

Rights: Copyright © 2002 Institute of Mathematical Statistics

JOURNAL ARTICLE
28 PAGES


SHARE
Vol.30 • No. 3 • July 2002
Back to Top