任意连续型随机变量序列关于广义赌博系统的一类强偏差定理

A class of strong deviation theorems on generalized gambling system for the sequence of arbitrary continuous random variables

设{Xn,n≥0}是任意相依的连续型随机变量序列,{Yn,n≥1}为一列广义随机选择函数.{Bn,n≥0}是实直线上的Borel集,IBn为Bn的示性函数.文中采用构造n元乘积密度函数及非负上鞅的方法,研究{YnIBn(Xn),n≥1}的极限性质,得到相依连续型随机变量序列的一类强偏差定理,其偏差依赖于样本点.

Let {Xn,n≥0}be an arbitrary sequence of dependent continuous random variables,{Yn,n≥1}be a series of generalized random selection functions,{Bn,n≥0} be Borel sets on the real line,and IBnbe the indicator function of Bn.The limit properties of {YnIBn（Xn）,n≥1} are studied by constructing n variable product density functions and super martingale,and a class of strong deviation theorems represented by the equalities are obtained.The bounds of the deviation depend on sample points.