任意随机序列关于连续型非齐次马氏链的一类强偏差定理

摘要

By using the notion of asymptotic logarithm likelihood ratio,a class of strong deviation theorems for the indicator function of Borel sets on the real line of arbitrary sequence was studied,with dependent continuous random variables on the distribution function of the continuous nonhomogeneous Markov chain.The limit properties of the indicator function of Borel sets on the real line was investigated by constructing variable product density functions and a nonnegative super martingale.A class of strong limit theorems represented by the inequalities was obtained as well.The results showed that the bounds of the deviation should be dependent on the sample points.%通过引入渐近对数似然比的概念,研究任意相依的连续型随机变量序列在实直线上的Borel集的示性函数关于连续性非齐次马氏链分布函数的一类强偏差定理.采用构造元乘积密度函数及非负上鞅的方法,研究实直线上的Borel集的示性函数的一类极限性质,得到相依连续型随机变量序列的一类以不等式表示的强极限定理,其偏差依赖于样本点.