设{Xn,n≥1}是同分布的~ρ混合序列,记Sn=^n∑i=1Xi.该文讨论了max1≤i≤n|Si|/i(n≥1)的分布函数的上界.作为应用,获得了随机变量supn≥1|Sn|/n1阶矩及p(〉1)阶矩分别存在有限的充分必要条件,这是一个与独立同分布场合相一致的结果。
Let {Xn,n≥1} be a sequence of identically distributed ~ρ mixing random variables and Sn=^n∑i=1Xi(n≥1). The paper discusses the upper bound of the distributions of max1≤i≤n|Si|/i(n≥1), and the sufficient and necessary conditions of the 1-th and p-th(p 〉 1) moments of supn≥1|Sn|/n1 are obtained, which are as same as the case of the independent identically distributions.