Laws of the iterated logarithm for the range of random walks in two and three dimensions

Richard F. Bass; Takashi Kumagai

doi:10.1214/aop/1029867131

Laws of the iterated logarithm for the range of random walks in two and three dimensions

Richard F. Bass^*, Takashi Kumagai

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

Abstract

Let S_n be a random walk in Z^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.

Original language	English
Pages (from-to)	1369-1396
Number of pages	28
Journal	Annals of Probability
Volume	30
Issue number	3
DOIs	https://doi.org/10.1214/aop/1029867131
Publication status	Published - 2002 Jul
Externally published	Yes

Keywords

Almost sure invariance principle
Intersection local time
Law of the iterated logarithm
Range of random walk

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/aop/1029867131

Cite this

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title = "Laws of the iterated logarithm for the range of random walks in two and three dimensions",

abstract = "Let Sn be a random walk in Zd and let Rn be the range of Sn. We prove an almost sure invariance principle for Rn when d = 3 and a law of the iterated logarithm for Rn when d = 2.",

keywords = "Almost sure invariance principle, Intersection local time, Law of the iterated logarithm, Range of random walk",

author = "Bass, {Richard F.} and Takashi Kumagai",

year = "2002",

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AU - Kumagai, Takashi

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KW - Almost sure invariance principle

KW - Intersection local time

KW - Law of the iterated logarithm

KW - Range of random walk

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Laws of the iterated logarithm for the range of random walks in two and three dimensions

Abstract

Keywords

ASJC Scopus subject areas

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