PA序列乘积部分和序列的极大值不等式和矩不等式

Maximal and Moment Inequalities for the Partial Sums of Sequences of the Product of PA Sequences

令T_n=∑ni=1X_iY_i,n≥1,这里{X_n,n≥1}是一列随机变量序列,{Y_n,n≥1}是一列相互独立的非负随机变量序列,且独立于X_i.文献[9]给出了当{X_n,n≥1}是一个NA序列时,关于T_n的一些极大值不等式.经证明,给出了当{X_n,n≥1}是一个PA序列时,关于T_n的Chow型和Doob型极大值不等式和一个矩不等式.

Let T_n=∑ni=1X_iY_i,n≥1,where{X_n,n≥1}is a sequence of random variables,and{Y_n,n≥1}is a sequence of nonnegative,independent random variables and independent of the X_i s.In 2012,some maximal inequalities are established for T_n by Christofdes and Hadjikyriakou when{X_n,n≥1}is a negatively associated sequence.In this paper,Chow type and Doob type maximal inequalities and a moment inequality are obtained for T_n when{X_n,n≥1}is a positively associated sequence.