【摘要】 设{xn,m≥1}是独立同分布随机变量序列,EX1=0,EX12=1．设Tn= Tn(X1,…,Xn)是随机函数且Tn=Sn+Rn．本文证明在E|Rn|2∨r<∞或E|Rn|<∞下,对随机函数Tn成立着Baum-Katz强大数律和重对数律的精确极限性质的一般结果．由此作为推论,对U-统计量,Von-Mises统计量,线性过程,移动平均过程,线性模型中误差方差估计和功率和等在适当矩条件下均可写出Baum-Katz强大数律和重对数律的精确极限性质．更多还原

【Abstract】 Let {Xn, -∞< n <∞} be a sequence of independent identically distributed random variables with EX1 = 0, EA12 = 1 and let , and Tn = Tn(X1,…, Xn) be a statistic (or random functions) such that: Tn = Sn + Rn. This paper gives an universal result in precise asymptotic of the Baum-Katz laws of large numbers and the law of iterated logarithms for Tn under some moment condition, such as E|Rn|2∨r <∞or E|Rn| <∞. As a consequence, it can be shown that the precise asymptotic of the LLN and LIL hold for U -statistics, Von-Mises statistics, linear processes, moving average processes, error variance estimates in linear models and power sums etc.更多还原