Strong laws of large numbers for arrays of rowwise independent random elements

Robert Lee Taylor and Tien-Chung Hu

International Journal of Mathematics and Mathematical Sciences, 1987, vol. 10, 1-10

Abstract:

Let { X n k } be an array of rowwise independent random elements in a separable Banach space of type p + δ with E X n k = 0 for all k , n . The complete convergence (and hence almost sure convergence) of n − 1 / p ∑ k = 1 n X n k to 0 , 1 ≤ p < 2 , is obtained when { X n k } are uniformly bounded by a random variable X with E | X | 2 p < ∞ . When the array { X n k } consists of i.i.d, random elements, then it is shown that n − 1 / p ∑ k = 1 n X n k converges completely to 0 if and only if E ‖ X 11 ‖ 2 p < ∞ .

Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:126351

DOI: 10.1155/S0161171287000899

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