ASYMPTOTIC PROPERTIES OF THE MOMENT CONVERGENCE FOR NA SEQUENCES

doi:10.1016/S0252-9602(14)60006-0

Abstract

Abstract:

It is well-known that the complete convergence theorem for i.i.d. random vari-ables has been an active topic since the famous work done by Hsu and Robbins [6]. Chow [4]obtained a moment version of Hsu and Robbins series. However, the series tends to infinity whenever ε goes to zero, so it is of interest to investigate the asymptotic behavior of the series
as ε goes to zero. This note gives some limit theorems of the series generated by moments for NA random variables.

Key words: Asymptotic property, rate of convergence, complete moment convergence, NA sequence

CLC Number:

60F15

ZHAO Yue-Xu. ASYMPTOTIC PROPERTIES OF THE MOMENT CONVERGENCE FOR NA SEQUENCES[J].Acta mathematica scientia,Series B, 2014, 34(2): 301-312.

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