■混合序列加权和的完全收敛性和强收敛性

随机变量取值的统计规律性往往通过大量的重复观测来体现,对大量重复观测作数学处理的常用方法是极限理论.独立同分布随机变量的极限理论已经很完善,近年来混合序列的极限理论发展较快,有的结果已接近独立同分布情形.讨论了一类较广泛的 φ混合序列加权和的收敛性质,获得了它的完全收敛性和强收敛性等性质.

Convergence for weighted sums of mixing random sequences

The study of statistical regularity of the random phenomenon is fundamental.After random variables introduced,the statistical regularity of the value-adopting of random variables is studied.This kind of statistical regularity is often reflected through enormous duplicated observations,in which the commonly used method is limiting principle during the mathematical process. Limiting principle for i.i.d random sequences is perfect.Limiting principle for mixing random sequences has achieved good result lately.In this paper the convergence properties of -mixing random sequences are studied.As a result,convergence for weighted sums of mixing random sequences is obtained.