中文摘要：

关于一列独立同分布正随机变量部分和乘积的几乎处处中心极限定理，已得出了结果．本文把独立性推广到相依随机变量的情形，在Ф-混合序列部分和乘积的渐近对数正态性基础上，以一个三角列的几乎处处中心极限定理为跳板，证明了在∑^∞n=1Ф^1：2（n）〈∞，且0〈σ0^2=1＋2∑^∞j=1E（X1-μ/σ）（Xj＋1-μ/σ）〈∞的条件下的几乎处处中心极限定理．

英文摘要：

The asymptotic behavior of product of the partial sums from a sequence of independent and identically distributed positive random variables has been studied. An almost sure central limit theorem for the product of subsequent partial sums of strictly stationary distributed square integarable is presented, positive J-mixing random variables under the condition of∑^∞n=1Ф^1：2（n）〈∞,and 0〈σ0^2=1＋2∑^∞j=1E（X1-μ/σ）（Xj＋1-μ/σ）〈∞.