Complete convergence for sums of arrays of random elements

Let {Xni} be an array of rowwise independent B-valued random elements and {an} constants such that 0<an↑∞. Under some moment conditions for the array, it is shown that ∑i=1nXni/an converges to 0 completely if and only if ∑i=1nXni/an converges to 0 in probability.

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Main Author: Soo Hak Sung
Format: Article
Language:English
Published: Wiley 2000-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S0161171200003112
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author Soo Hak Sung
author_facet Soo Hak Sung
author_sort Soo Hak Sung
collection DOAJ
description Let {Xni} be an array of rowwise independent B-valued random elements and {an} constants such that 0<an↑∞. Under some moment conditions for the array, it is shown that ∑i=1nXni/an converges to 0 completely if and only if ∑i=1nXni/an converges to 0 in probability.
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institution Kabale University
issn 0161-1712
1687-0425
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publishDate 2000-01-01
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series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-c35988f98ebf491d9bfeab28e4bc1f532025-02-03T06:11:21ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-01231178979410.1155/S0161171200003112Complete convergence for sums of arrays of random elementsSoo Hak Sung0Department of Applied Mathematics, Pai Chai University, Taejon 302-735, South KoreaLet {Xni} be an array of rowwise independent B-valued random elements and {an} constants such that 0<an↑∞. Under some moment conditions for the array, it is shown that ∑i=1nXni/an converges to 0 completely if and only if ∑i=1nXni/an converges to 0 in probability.http://dx.doi.org/10.1155/S0161171200003112
spellingShingle Soo Hak Sung
Complete convergence for sums of arrays of random elements
International Journal of Mathematics and Mathematical Sciences
title Complete convergence for sums of arrays of random elements
title_full Complete convergence for sums of arrays of random elements
title_fullStr Complete convergence for sums of arrays of random elements
title_full_unstemmed Complete convergence for sums of arrays of random elements
title_short Complete convergence for sums of arrays of random elements
title_sort complete convergence for sums of arrays of random elements
url http://dx.doi.org/10.1155/S0161171200003112
work_keys_str_mv AT soohaksung completeconvergenceforsumsofarraysofrandomelements