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

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 resul...

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Bibliographic Details
Published in:Acta mathematica Hungarica 2019-04, Vol.157 (2), p.312-326
Main Authors: Thanh, L. V., Thuy, N. T.
Format: Article
Language:English
Subjects:
Banach spaces
Convergence
Mathematics
Mathematics and Statistics
Sharpness
Sums
Theorems
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Summary: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.
ISSN:0236-5294
1588-2632
DOI:10.1007/s10474-018-0876-x