中文摘要：

关于一列独立同分布正随机变量部分和乘积的渐近性性质,已得出了一系列结果.本文把独立性推广到相依随机变量的情形,对一列强平稳平方可积的正φ-混合序列{Xn,n≥1}进行讨论,若满足∑∞n=1φ1/2（n）＜∞且0＜σ20=1＋2∑∞j=1E（X1-μ）/（σ）（Xj＋1-μ）/（σ）＜∞.则其部分和的乘积渐近对数正态.

英文摘要：

The asymptotic behavior of product of the partial sums from a sequence of independent and identically distributed positive random variables have been studied by several papers. It is proved that the product of subsequent partial sums of strictly stationary distributed square integarable, positive φ-mixing random variables is asymptotically lognormal under the condition of ∑∞n=1φ1/2（n）〈∞且0〈σ20=1＋2∑∞j=1E（X1-μ）/（σ）（Xj＋1-μ）/（σ）〈∞.