Abstract
For double arrays of constants {a ni, 1≤i≤k n, n≥1} and NA r.v. 's {X n, n≥1}, conditions for almost sure convergence of \(\sum\limits_{i = 1}^{k_n } {a_{ni} X_i } \) are given. Both casesk n ↑ ∞ andk n=∞ are treated. A Marcinkiewicz-type theorem for i. d. NA sequences is obtained as a special case.
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References
Joag-Dev K, Proschan F. Negative association of random variable with applications.Ann Statist, 1983,11(1):286–295.
Choi B D, Sung S H. Almost sure convergence theorem of weighted sums of random variables.Stoch Ann& Appl, 1987,5(4):365–377.
Matula P. A note on the almost sure convergence of sums of negatively dependent random variables.Stast Probab Lett, 1992,15(3):209–213
Gan S X. The Hajek-Renyi inequality for Banach space valued random sequence and its application.Wuhan Uni J Natur Sci. 1997,2(1):13–18
Teicher H. Generalized exponential bounds, iterated logarithm and strong laws.Z Warhrsch Verw Geb, 1979,48: 293–307.
Teicher H. Almost certain convergence in double arrays.Z Warhrsch Verw Geb, 1985,69:331–345
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Supported by the National Natural Science Foundation of China
Cheng Riyan: born in 1968, MS student
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Riyan, C., Shixin, G. Almost sure convergence of weighted sums of NA sequences. Wuhan Univ. J. Nat. Sci. 3, 11–16 (1998). https://doi.org/10.1007/BF02827504
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DOI: https://doi.org/10.1007/BF02827504