多元随机序列泛函的强偏差定理

A Strong Deviation Theorem of Functional for Multivariate Random Sequences

利用熵密度和样本偏差率的概念,建立了多元随机序列泛函关于条件期望的用不等式表示的强极限性质(称之为强偏差定理),在推论部分得到了非齐次马氏链的强偏差定理和随机条件概率的调和平均值的极限性质等相关结论.证明中给出了将条件矩母函数应用于研究多元随机序列泛函的强极限性质的一种途径.

A strong deviation theorem of functional for multivariate random sequences with respect to conditional expectation is established by using the notion of entropy density and sample divergence rat. The corollaries include a strong deviation theorem for nonhomogenous Markov chains and a limit property for the harmonic mean of random conditional probabilities. In the proof, an approach of applying the conditional moment generating function to the investigation of the strong limit property on multivariate random sequences is proposed.