Exact Strong Laws for Multidimensionally Indexed Random Variables

André Adler

Journal of Multivariate Analysis, 2001, vol. 77, issue 1, 73-83

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

Keywords: almost sure convergence; strong law of large numbers; slow variation (search for similar items in EconPapers)
Date: 2001
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