A Class Of Strong Laws Of Large Numbers And Strong Stability Of Linear Forms For AQSI Sequences

AQSI sequences are wide range of random sequences found by Ghosal and Chandra.Independent sequences can be seen as a special situation of AQSI se-quences.So it attracts many scholars' attention.And its related results can be better used in practical problem of mathematical statistics.Probability limit theories in independent random sequences has gained a quite perfect develop-ment.Samples in most cases is not independent in statistical problems.The relative functions of the independent samples are not independent.We some-times weaken the conditions of independence.AQSI sequences are wider range of random sequences than independent sequences.Because of their wide range of conditions,it becomes more difficult to study their characters.So it's more meaningful to study them.This paper mainly consists of two parts.In the first part,we study the strong law of large numbers of partial sum and sum of products in AQSI sequences.Then we obtain the sufficient conditions for the strong law of large numbers of partial sum and sum of products in AQSI sequences.In the second part,we study the strong stability of linear forms in AQSI sequences,which is based on a class of strong laws of large numbers for AQSI sequences.Then we get the sufficient conditions for strong stability of linear forms in different distributions AQSI sequences.We introduce the first part of the paper.On the one hand,most scholars devote to studying the properties of partial sum,it contributes to neglecting the properties of sum of products.On the other hand,as a special kind of U statistics,sum of products is related to partial sum,and it is also different from partial sum.So it is necessary to research the properties of sum of products.This part emphasis studying the strong law of large numbers of partial sum and sum of products in AQSI sequences,and it gets some important theories.The results of this paper are of great importance.Lastly,we introduce the second part of this paper.When we study the compatibility of the least squares estimate of a linear model,we need to dis-cuss strong stability of linear forms,so it is of great significiance.This part discusses the strong stability of linear forms in AQSI sequences,and it gets some important theories.The results of this paper has a certain application value.