On the almost certain limiting behavior of normed sums of identically distributed positive random variables

Andrew Rosalsky

Statistics & Probability Letters, 1993, vol. 16, issue 1, 65-70

Abstract: Consider a sequence of identically distributed positive random variables {Xn, n [greater-or-equal, slanted] 1} with partial sums Sn = [summation operator]nj = 1, Xj, n [greater-or-equal, slanted] 1, and let {bn & 0, n [greater-or-equal, slanted] 1} be a sequence of norming constants. The almost certain limiting behavior of the normed sums Sn/bn is investigated irrespective of the joint distributions of the {Xn, n [greater-or-equal, slanted] 1}. Some open problems are also formulated. The current investigation was inspired by that of Smit and Vervaat (1983) on the convergence of series of nonnegative random variables irrespective of the joint distributions of the random variables.

Keywords: Identically; distributed; positive; random; variables; normed; sums; almost; certain; limiting; behavior; strong; law; of; large; numbers; irrespective; of; the; joint; distributions (search for similar items in EconPapers)
Date: 1993
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Citations: View citations in EconPapers (4)

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