$φ$-混合序列加权和的完全收敛性

Abstract

Abstract:

The paper obtains the complete convergence for the maximun weighted sums, which improved and extended the result of Chen and Sung[1] from NA sequence to $φ$ -mixing random variables. The main tool in Chen and Sung[1] is the exponent inequality of NA sequence, but no one knows wether the coresponding exponent inequality holds or not for $φ$ -mixing random variables, so a different method is needed. In fact, we use only the maximun moment inequality and a new truncated method to prove the main result.

Key words: $φ$ -Mixing sequence ')"> $φ$ -Mixing sequence , Weighted sum, Complete convergence

CLC Number:

O211.4

Zhihua Zhang,Pingyan Chen. Complete Convergence for Weighted Sums for $φ$ -Mixing Random Variables[J].Acta mathematica scientia,Series A, 2018, 38(6): 1095-1102.

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References 15

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Complete Convergence for Weighted Sums for $φ$ -Mixing Random Variables

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Complete Convergence for Weighted Sums for $φ$ -Mixing Random Variables