Strong Convergence For The Some Dependent Random Variables Sequences

Let { X ,Xn ,n≥0} be a sequence of pairwise independent distributed random variables, 1 < p <2.In the first chap- ter, the paper obtains the convergent rate of Cesàro stro- ng law of large number under the conditions reα>1. In order to prove this result, the paper discu- sses the convergent rate of Cesàro strong law of large number for the sequence of pairwise negative correlati- onal random variables and its is interested. The result also holds for identically distributed pairwise NQD se- quences.In the second chapter ,we discuss some main results in the article, as corollary, the given result is the particular cases of the result of this paper. And we also obtain in the generallization of some related corollarie- s.In the third chapter,a new concept of integrability (known as strong h-integrability) is introduced for an array of random variables concerning an array of constan- ts. Under this condition of integrability, we tudy the strong law of an array of rowwise NQD random variables, and obtain the results: Sa( XEX)0a.s., where { X nk ,un≤k≤vn} be an array of rowwise NQD random variables and {a nk ,un≤k≤vn} an array of constants, which improve the results of Ceabrena(2005) and we finally discuss the same problem about non-negative random varibles, and obtain the similar results.