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Almost surely convergent summands of a random sum

Author

Listed:
  • Chobanyan, S.
  • Levental, S.
  • Mandrekar, V.

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.

Suggested Citation

  • Chobanyan, S. & Levental, S. & Mandrekar, V., 2012. "Almost surely convergent summands of a random sum," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 212-216.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:1:p:212-216
    DOI: 10.1016/j.spl.2011.09.017
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    Keywords

    Symmetrizations; Convergence almost surely;

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