A generalization of the Petrov strong law of large numbers

Valery Korchevsky

Statistics & Probability Letters, 2015, vol. 104, issue C, 102-108

Abstract: In 1969 V.V. Petrov found a new sufficient condition for the applicability of the strong law of large numbers to sequences of independent random variables. He proved the following theorem: let {Xn}n=1∞ be a sequence of independent random variables with finite variances and let Sn=∑k=1nXk. If Var(Sn)=O(n2/ψ(n)) for a positive non-decreasing function ψ(x) such that ∑1/(nψ(n))<∞ (Petrov’s condition), then the relation (Sn−ESn)/n→0 a.s. holds.

Keywords: Strong law of large numbers; Sequences of independent random variables; Dependent random variables (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spl.2015.05.010

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