ρ-混合随机变量序列加权和的完全收敛性质

摘要

应用ρ-混合随机变量序列截断法、Hölder 不等式、Markov 不等式、Jensen 不等式、Cr不等式及ρ-混合随机变量的Rosenthal型矩不等式，考察在没有同分布假设条件下，ρ-混合随机变量序列加权和的完全收敛性质，并利用 Borel-Cantelli 引理，给出ρ-混合随机变量序列加权和的Marcinkiewicz-Zygmund型强大数定律。%The authors studied the complete convergence for weighted sums ofρ--mixing random variables sequence without assumption of identical distribution via truncation method forρ--mixing random variables sequence,Hölder inequality,Markov inequality,Jensen inequality,Cr inequality, moment inequality and Rosenthal inequality.As an example of application,we further extended the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums ofρ--mixing random variables sequence with the aid of Borel-Cantelli lemma.