Some Limit Properties For φ Mixing Sequence With Application

φ mixing sequence is a kind of very extensive random variables sequence and contains independent sequences as its special cases. φ mixing sequences has been widely used in many fields, such as reliability theory, seepage theory, multivariate statistical analysis and so on, therefore, many scholars are interested in the limit properties of φ mixing sequence.Making use of some conditions of classical independent random variables sequences limit properties, we discuss the limit properties of φ mixing sequence and get the conclusion that the limit properties is similar to independent case, at the same time, we generalize the some existing conclusions.This paper is divided into two parts, the first part elaborates Kolmogorov inequalities of φ mixing sequence in some of the more weak conditions and uses it to obtain the strong law of large numbers of partial sum and sum of products for φ mixing sequence. In the second part, we discuss the complete convergence of weighted sum for φ mixing sequence with simple condition and extend the results which are established in article. As its application, we give a sufficient condition of the strong consistency of regression function estimator for φ mixing sequence.