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Complete convergence for sums of arrays of random elements

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  • Soo Hak Sung

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.

Suggested Citation

  • Soo Hak Sung, 2000. "Complete convergence for sums of arrays of random elements," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 23, pages 1-6, January.
    • Handle: RePEc:hin:jijmms:939278
    DOI: 10.1155/S0161171200003112
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