强φ-mixing变量和的收敛定理

THE CONVERGENT THEOREMS OF SUMS OF STRONG φ-MIXING VARIABLES

若强φ-mixing序列{Z_i,i≥1}有Esup■|Z_i|=0(1),n→∞,S_n为L_1-收敛,n→∞。则S_n,a.s.收敛。

If strong Φ-mixing sequence {X_i, i≥1} satisfy ■|X_i|=0(1). n→∞. S_n∈L_1, then S_n converges almost surely.