Almost surely convergent summands of a random sum

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.

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Year of publication:	2012
Authors:	Chobanyan, S. ; Levental, S. ; Mandrekar, V.
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 82.2012, 1, p. 212-216
Publisher:	Elsevier
Subject:	Symmetrizations \| Convergence almost surely

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

Persistent link: https://www.econbiz.de/10010582244