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Acta Mathematica Hungarica

, Volume 157, Issue 2, pp 312–326 | Cite as

Necessary and sufficient conditions for complete convergence of double weighted sums of pairwise independent identically distributed random elements in Banach spaces

  • L. V. ThanhEmail author
  • N. T. Thuy
Article
  • 37 Downloads

Abstract

This paper provides necessary and sufficient conditions for complete convergence of double weighted sums of pairwise independent identically distributed random elements in Banach spaces. The main theorem extends Theorem 1.2 in [1] to the double weighted sum setting. The sharpness of the main result is illustrated by showing that the main theorem can fail if we replace the identical distribution condition by a slightly weaker condition, even when the random elements are independent and uniformly almost surely bounded.

Key words and phrases

complete convergence double array weighted sum pairwise independent random element Banach space 

Mathematics Subject Classification

60B11 60B12 60F15 

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Notes

Acknowledgement

The authors are grateful to Professor Andrew Rosalsky for reading the first draft of the paper and giving very helpful comments.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Department of MathematicsVinh UniversityVinh CityVietnam

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