A note on the strong law of large numbers for associated sequences

A. Nezakati

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-4

Abstract:

We prove that the sequence { b n − 1 ∑ i = 1 n ( X i − E X i ) } n ≥ 1 converges a.e. to zero if { X n , n ≥ 1 } is an associated sequence of random variables with ∑ n = 1 ∞ b k n − 2 Var ( ∑ i = k n − 1 + 1 k n X i ) < ∞ where { b n , n ≥ 1 } is a positive nondecreasing sequence and { k n , n ≥ 1 } is a strictly increasing sequence, both tending to infinity as n tends to infinity and 0 < a = inf n ≥ 1 b k n b k n + 1 − 1 ≤ sup n ≥ 1 b k n b k n + 1 − 1 = c < 1 .

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:126390

DOI: 10.1155/IJMMS.2005.3195

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