φ-混合随机变量序列加权和的完全收敛性及完全矩收敛性

Complete Convergence and Complete Moment Convergence for Weighted Sums ofφ-mixing Random Variables

【目的】对φ-混合随机变量序列的完全收敛性和完全矩收敛性进行讨论。【方法】利用φ-混合随机变量序列的Rosenthal型极大值不等式。【结果】建立了φ-混合随机变量序列加权和的完全收敛性,并且在同样的条件下得到了φ-混合序列的完全矩收敛性。【结论】所得结果推广并改进了已有文献中关于NA序列相应的结果。

[Purposes]The main purpose of this paper is to establish the complete convergence and complete moment convergence for the weighted sums of φ-mixing random variables. [Methods]The main results are obtained by using the Rosenthat-type maximum inequality of φ-mixing random variables. [Findings]The complete convergence is successfully established for the weighted sums of φ-mixing random variables and moreover the complete moment convergence is obtained without adding any extra conditions. [Conclusions]The results extend and improve the corresponding one of Sung for NA random variables to φ-mixing random variables.