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隐非齐次马尔可夫模型的强大数定律 被引量：1

STRONG LAW OF LARGE NUMBER OF HIDDEN NONHOMOGENEOUS MARKOV MODELS
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摘要 本文研究了一类隐非齐次马尔可夫模型的强极限定理.利用鞅差序列收敛定理,获得了观测链{Y_n,n≥0}的强大数定律,并给出了观测链的Shannon-McMillan定理. In this article,the strong limit theorem of hidden nonhomogeneous Markov models is discussed.By the martingale difference theorem,the strong law of large number of the observed chain is proved,and the Shannon-McMillan theorem of the observed chain is given.
作者 吴小太 杨卫国
机构地区 安徽工程科技学院数学系 江苏大学理学院
出处 《数学杂志》 CSCD 北大核心 2011年第2期314-322,共9页 Journal of Mathematics
基金 国家自然科学基金资助(10571076 10826098)
关键词 隐马尔可夫模型 非齐次马尔可夫链 强大数定律 ＊-混合 hidden Markov models nonhomogeneous Markov chain strong law of large numbers ＊-mixing
分类号 O211.6 [理学—概率论与数理统计]
  • 相关文献

参考文献11

  • 1Ephraim Y, Merhav N. Hidden Markov processes[J]. IEEE Trans. Inf. Theory, 2002, 48(6): 1518-1569.
  • 2Leroux B G. Maximum-likelihood estimation for hidden Markov models[J]. Stochastic Process Appl., 1992, 40:127-143.
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同被引文献11

  • 1龚光鲁,钱敏平.应用随机过程[M].北京:清华大学出版社,2004.
  • 2Lacrz B, Lasala P, Lekuona A. Dynamic graphical models and nonhomogeneous hidden Markov models [J].Stat. Probab. Letts., 2000,49:377-385.
  • 3Bates B C, Charles S P, Hughes P. Stochastic downscaling of numerical climate model simulations [J].Envrionmental Modelling Software, 1998,13:325-331.
  • 4Leroux B G. Maximum-likelihood estimation for hidden Markov models [J]. Stochastic Processes and theirAppl., 1992,40:127-143.
  • 5Bickel P, Ritov Y, Ryden T. A smptotic normality of the maximum-likelihood estimation for general hiddenMarkov models [J]. The Annals of Statistics, 1998,26(4):1614-1635.
  • 6Ephrain Y, Merhav N. Hidden Markov process [J]. 2002,48(6):1518-1569.
  • 7Chung K L. A Course in Probability Theory [M]. 2nd ed, New York: Academic Press, 1974.
  • 8Yang W G. The asymptotic equipartition property for a nonhomogeneous Markov information source [J].Probability in the Engineering and Informational Science, 1998,12:509-518.
  • 9Yang W G. Convergence in the cesaro sense and strong law of large numbers for countable nonhomogeneousMarkov chains [J]. Linear Algebra and its Application, 2002,354:275-286.
  • 10Yang W G. Strong law of large numbers for countable nonhomogeneous Markov chains [J]. Linear Algebraand its Application, 2009,430:3009-3018.

引证文献1

数学杂志
2011年 第2期

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