Exact Strong Laws for Multidimensionally Indexed Random Variables

Consider independent and identically distributed random variables {X,Â Xn,Â n[set membership, variant]Zd+} with either EX=0 or EÂ X=[infinity]. We establish strong laws so that [summation operator]n[less-than-or-equals, slant]NÂ anXn/bN-->1 almost surely. Our procedure selects the constants {an,Â n[set membership, variant]Zd+} and {bN,Â N[greater-or-equal, slanted]1} so that these strong laws obtain in almost any possible setting.

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Year of publication:	2001
Authors:	Adler, André
Published in:	Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 77.2001, 1, p. 73-83
Publisher:	Elsevier
Subject:	almost sure convergence \| strong law of large numbers \| slow variation

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005153275