三重循环马氏链的强大数定律

doi:10.3969/j.issn.1671-7775.2010.003.026

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摘要为了研究一类非齐次马氏链——循环马氏链的强极限定理,首先考虑到非齐次马氏链的转移矩阵是循环的情形经常出现,从而引进了三重循环马氏链的概念,然后利用非齐次马氏链函数的极限性质推导出三重循环马氏链关于状态出现频率的极限性质,并利用该性质得到了三重循环马氏链关于状态出现频率的强大数定律,为循环马氏链的应用提供了理论依据.

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	杨卫国
	梁佩佩

关键词 ：三重循环马氏链')" href="#">Type=K">三重循环马氏链, 状态频率')" href="#">Type=K">状态频率, 遍历')" href="#">Type=K">遍历, 转移矩阵')" href="#">Type=K">转移矩阵, 强大数定律')" href="#">Type=K">强大数定律

Abstract：In order to study the strong limit theorems for circular Markov chains in nonhomogenous Markovchains,firstly,the definition of three-order circular Markov chains is introduced.Then by applyingthe limit property for functions of nonhomogenous Markov chains,the limit property for the frequenciesof occurrence of states for three-order circular Markov chains is established.Finally,the strong law of large numbers on the frequencies of occurrence of states for three-order circular Markov chains is obtained,which offers a theoretical basis for the applications of circular Markov chains

Key words： three-order circular Markov chains ')" href="#">three-order circular Markov chains state frequency ')" href="#">state frequency strong ergodic')" href="#">strong ergodic transition matrix')" href="#">transition matrix strong law of large numbers ')" href="#">strong law of large numbers

基金资助:

国家自然科学基金资助项目（10571076）

引用本文:

杨卫国, 梁佩佩. 三重循环马氏链的强大数定律[J]. 江苏大学学报（自然科学版）, 2010, 31(3): 369-372. Yang Weiguo, Liang Peipei. Strong law of large numbers for three-order circular Markov chains[J]. Journal of Jiangsu University(Natural Science Eidtion) , 2010, 31(3): 369-372.

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http://zzs.ujs.edu.cn/xbzkb/CN/10.3969/j.issn.1671-7775.2010.003.026 或 http://zzs.ujs.edu.cn/xbzkb/CN/Y2010/V31/I3/369