| m阶马氏链关于广义随机选择系统的极限定理 |
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| 引用本文： | 宗德才,王康康.m阶马氏链关于广义随机选择系统的极限定理[J].数学的实践与认识,2014(16). |
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| 作者姓名： | 宗德才 王康康 |
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| 作者单位： | 常熟理工学院计算机科学与工程学院;江苏科技大学数理学院; |
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| 基金项目： | 江苏省高校自然科学基金(09KJD110002) |
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| 摘 要： | 主要研究广义随机选择系统中的m阶非齐次马氏链随机转移概率调和平均的a.s.收敛的强极限定理.在证明中采用了一种把网微分法与条件矩母函数相结合应用于马氏链强极限定理研究的新途径.作为推论,得到m阶非齐次马氏链随机条件概率一个公平比的强极限定理,并将已有的结果加以推广.
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| 关 键 词： | m阶非齐次马氏链 调和平均 网微分法 条件矩母函数 广义随机选择系统 |
The Limit Theorems for mth-order Nonhomogeneous Markov Chains on the Generalized Random Selection System |
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| Abstract: | In this paper,we study the strong limit theorems on the a.s.convergence for the harmonic mean of the mth-order nonhomogeneous Markov chain in the generalized random selection system.In the proof,we apply the tools of the conditional moment generating functions and the differentiation on a net to the study of strong limit theorems for the mthorder nonhomogeneous Markov chain.As corollaries,a limit theorem for fair ratio of mth-order non- homogeneous Markov chains is obtained.Moreover,the results which have been obtained are generalized. |
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| Keywords: | mth-order nonhomogeneous Markov chains harmonic mean the differentiation on a net the conditional moment generating functions the generalized random selection system |
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