Almost surely convergent summands of a random sum

S. Chobanyan, S. Levental and V. Mandrekar

Statistics & Probability Letters, 2012, vol. 82, issue 1, 212-216

Abstract: We find a sufficient condition for a.s. convergence to zero of summands given that a sum of two sequences of random variables a.s. converges to zero. The condition turns out to be weaker than that used in the monograph by Loeve and in a paper by Martikainen. Our result is also used in construction of a counter-example regarding the a.s. convergence of a rearranged series.

Keywords: Symmetrizations; Convergence almost surely (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spl.2011.09.017

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