非平稳φ-混合序列强律收敛速度的进一步探讨

A Further Discussion on The Covergence Rates of The Strong Law for Non Stationary φ mixing Squences

本文研究非平稳φ混合序列的强大数律：无需混合速度限制，给出了完全收敛成立的充要条件；在弱混合速度条件下，讨论了ＭａｒｃｉｎｋｉｅｗｉｃｚＺｙｇｍｕｎｄ强律成立的必要条件，进而得出混合情形的ＭａｒｃｉｎｋｉｅｗｉｃｚＺｙｇｍｕｎｄ强律，其结果与独立情形相一致．

In this paper we further investigate the strong law for non stationary Φ mixing sequences. Firstly, without any mixing rates, we obtain the sufficient and necessary condition of the complete convergence. Secondly, under the weak condition of mixing rates, we discuss the necessary condition of the Marcinkiewicz Zygmund strong law and obtain the strong law for Φ mixing sequences. The main results are simular to those of independent sequences.