Exact strong laws for multidimensionally indexed random variables

Authors
Adler, A
Citation
A. Adler, Exact strong laws for multidimensionally indexed random variables, J MULT ANAL, 77(1), 2001, pp. 73-83
Citations number
10
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF MULTIVARIATE ANALYSIS
ISSN journal
0047259X → ACNP
Volume
77
Issue
1
Year of publication
2001
Pages
73 - 83
Database
ISI
SICI code
0047-259X(200104)77:1<73:ESLFMI>2.0.ZU;2-K
Abstract
Consider independent and identically distributed random variables {X, X-n, n is an element of Z(+)(d)} with either EX = 0 or E \X\ = x. We establish s trong laws so that Sigma (\n\ less than or equal to N) a(n)X(n). b(N) --> 1 almost surely. Our procedure selects the constants {a(n), n is an element of Z(+)(d)} and {b(N), N greater than or equal to 1} so that these strong l aws obtain in almost any possible setting. (C) 2001 Academic Press.