The Annals of Probability
- Ann. Probab.
- Volume 30, Number 3 (2002), 1369-1396.
Law of the iterated logarithm for the range of random walks in two and three dimensions
Richard F. Bass and Takashi Kumagai
Full-text: Open access
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 $d=2$.
Article information
Source
Ann. Probab., Volume 30, Number 3 (2002), 1369-1396.
Dates
First available in Project Euclid: 20 August 2002
Permanent link to this document
https://projecteuclid.org/euclid.aop/1029867131
Digital Object Identifier
doi:10.1214/aop/1029867131
Mathematical Reviews number (MathSciNet)
MR1920111
Zentralblatt MATH identifier
1031.60031
Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60F15: Strong theorems 60G17: Sample path properties
Keywords
Range of random walk law of the iterated logarithm law of the iterated logarithm intersection local time
Citation
Bass, Richard F.; Kumagai, Takashi. Law of the iterated logarithm for the range of random walks in two and three dimensions. Ann. Probab. 30 (2002), no. 3, 1369--1396. doi:10.1214/aop/1029867131. https://projecteuclid.org/euclid.aop/1029867131
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- STORRS, CONNECTICUT 06269 E-MAIL: bass@math.uconn.edu RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES Ky OTO UNIVERSITY Ky OTO 606-8502 JAPAN E-MAIL: kumagai@kurims.ky oto-u.ac.jp

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