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| 多元随机序列泛函的强偏差定理 | |
| 引用本文： | 檀亦丽,万星火,姜君娜,李颖. 多元随机序列泛函的强偏差定理[J]. 数学的实践与认识, 2009, 39(9) |
| 作者姓名： | 檀亦丽 万星火 姜君娜 李颖 |
| 作者单位： | 河北理工大学,理学院,河北,063009 |
| 基金项目： | 河北省自然科学基金，河北理工大学科学研究基金 |
| 摘 要： | 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. |
| 关 键 词： | 熵密度 样本偏差率 条件矩母函数 强偏差定理 |
A Strong Deviation Theorem of Functional for Multivariate Random Sequences |
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| TAN Yi-li,WAN Xing-huo,JIANG Jun-na,LI Ying. A Strong Deviation Theorem of Functional for Multivariate Random Sequences[J]. Mathematics in Practice and Theory, 2009, 39(9) | |
| Authors: | TAN Yi-li WAN Xing-huo JIANG Jun-na LI Ying |
| Abstract: | 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. |
| Keywords: | Entropy density sample divergence rat conditional moment generating function strong deviation theorem |
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