关键词: 几乎处处中心极限定理, &rho, ^--混合序列, 部分和之和的乘积

Abstract:

Let {X,X_n}^_n∈N be a strictly stationary sequence of ρ^--mixing random variables, on the basis of which almost sure central limit theorem with  weight d_k=k^-1exp{log^αk}(0≤α<1/2) was obtained for the product of sums of partial sums by virtue of central limit theorem of weighted sums  and the moment inequality.

Key words: almost sure central limit theorem, ρ^--mixing sequences, product of sums of partial sums