【作者】 王晓丹；

【导师】 董志山；

【作者基本信息】 吉林大学 ， 应用数学， 2008， 硕士

【摘要】 在概率论中,对于随机变量的强收敛性及大数定律的讨论是具有重大意义的,许多学者都致力于这方面的研究.本文的目的是研究随机变量的强收敛性与强大数定律.首先研究了两两独立同分布序列Cesàro强大数定律的收敛速度.设{ X ,Xn ,n≥0}是两两独立同分布的随机变量序列, 1 < p <2.在条件EX =μ,EXp<∞下获得了阶数大于1的Cesàro强大数定律的收敛速度.其次又研究了NA随机变量序列强收敛性的相关结论.通过研究不同条件下NA随机变量序列的强收敛性的几个结论,将已有的某个结果进行推广,使之成为推论;并推广了NA随机变量序列在非同分布情形的结果,所得的结论充实了强极限方面的内容.最后研究了负相依随机变量阵列加权和的强收敛性.通过引入强h可积条件,讨论行内两两NQD阵列的强收敛性,得到结果,该结果强化了Ceabrena(2005)的结果.并讨论了一般非负随机变量阵列的情形,得到了类似的结果.更多还原

【Abstract】 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.更多还原