Strong Convergence Theorems And Its Applications For (?,?) Mixing

Probability limit theory is one of the main branch of probability and statistics discipline,also is the theoretical foundation of other branches of probability and mathematical statistics.Probability limit theory has been widely used in many fields,such as natural science,management science,biological science,engineering science,game theory,information and communication theory,economy and finance.In the actual problem,independence condition is difficult to meet,so probability and statistics experts have put forward and discussed the properties of various dependent sequence.Using some conditions of classical independent random variables sequences limit properties,we study the limit properties for(?,?)mixing sequence.It is a kind of very extensive sequence of random variables and contains independent sequences as its special cases.This paper is divided into two parts,the first part,we use Kolmogorov inequali-ties for(?,?)mixing sequence and end method to obtain the three series theorem and some convergence theoreoms,in some of the more weak conditions discussing strong law of large numbers of partial sum and sum of products for(?,?)mix-ing sequence.Furthermore,we extend properties of independent random sequences to the case(?,?)mixing sequence.In the second part,we discuss the complete convergence of weighted sum for(?,?)mixing sequence with simple condition.As application,we give a sufficient condition of the strong consistency of regression function estimator for(?,?)mixing sequence.