ф-Mixing变量和的极大不等式

THE MAXIMAL INEQUALlTY OF SUMS OF ф-MIXING VARIABLES

若M=1,ф(1)<1,则φ-mixing变量的部分和S_n成立不等式■S_n依概率收敛蕴含a.s.收敛;若ф(M)<1,有不等式■ε>0.5_n依概率收敛和■依概率收敛于0,当n→∞.蕴含a.s.收敛.

If M=1, ф(1)<1, Then Sums S_n of ф-mixing variables Satisfy ■ conver-gences in Probabilty then S_n a.s. convergences; If ф(M)<1, then ■ S_n convergences in Probability and ■ implies a.s. conver-gence.