Complete convergence for sums of arrays of random elements

Soo Hak Sung

International Journal of Mathematics and Mathematical Sciences, 2000, vol. 23, 1-6

Abstract:

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

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:939278

DOI: 10.1155/S0161171200003112

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