一类随机变量加权和的完全收敛性

摘要

设{X n ,n≥1}是一列满足 Rosenthal 型不等式的相依随机变量,在非同分布下建立了这类随机变量加权和的完全收敛性的新定理,并获得了相依随机变量加权和的强大数定律。所得结论把相应结果从独立同分布的情形扩展到普遍的相依变量情形。%Let {X n ,n≥1}be a sequence of dependent random variables which satisfied Rosenthal type inequality.We established some new complete convergence theorems for weighted sums of a class of random variables with different distributions,and obtained the strong laws of large numbers for weighted sums of dependent random variables.Our results extend the corresponding results from the independent identically distributed case to the universal dependent random variables.