两两NQD列的强收敛性质

Strong-convergence Properties for Pairwise NQD Random Sequences

本文讨论两两NQD随机变量列极限理论中的强收敛性质。首先建立了两两NQD随机变量列最大部分和的Bernstein型概率指数不等式;并在此基础上,给出了具有不同分布的两两NQD列在较弱矩条件下的Petrov型对数律与Wittmann型重对数律,将文献中相应内容从NA情形推广到两两NQD情形。

The main purpose of this paper is to discuss the strong-convergence properties about pairwise NQD sequences in the realm of limit theory, Firstly, the Berntein＇s exponential inequality of maximal partial sums for pairwise NQD random sequences is derived; and based on the inequality, we work out, under weak conditions on the moment restrictions, law of the Petrov＇s logarithm and law of the Wittmann＇s iterated logarithm for pairwise NQD sequences with different distribution functions, Some corresponding results in the literature are improved and extended from the NA case to the more general NQD case.