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Laws of the Iterated Logarithm for Triple Intersections of Three Dimensional Random Walks

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Laws of the Iterated Logarithm for Triple Intersections of Three Dimensional Random Walks
2.	Creator	Author's name, affiliation, country	Jay Rosen; College of Staten Island, CUNY
3.	Subject	Discipline(s)	Mathematics
3.	Subject	Keyword(s)	random walks, intersections
3.	Subject	Subject classification	60J15, 60F99
4.	Description	Abstract	Let $X = X_n, X' = X'_n$, and $X'' = X''_n$, $n\geq 1$, be three independent copies of a symmetric three dimensional random walk with $E(|X_1|^{2}\log_+ |X_1|)$ finite. In this paper we study the asymptotics of $I_n$, the number of triple intersections up to step $n$ of the paths of $X, X'$ and $X''$ as $n$ goes to infinity. Our main result says that the limsup of $I_n$ divided by $\log (n) \log_3 (n)$ is equal to $1 \over \pi |Q|$, a.s., where $Q$ denotes the covariance matrix of $X_1$. A similar result holds for $J_n$, the number of points in the triple intersection of the ranges of $X, X'$ and $X''$ up to step $n$.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	1997-03-26
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/16
10.	Identifier	Digital Object Identifier	10.1214/EJP.v2-16
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 2
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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