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Ergodicity for countable nonhomogeneous circular Markov chains |
Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China |
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Abstract The ergodicity for special nonhomogeneous Markov chains of circular Markov chains was stu-died. The definitions of strong ergodicity and C-strong ergodicity of Markov chains were introduced. The definition of countable nonhomogeneous circular Markov chain was introduced with the consideration of circular transition matrix of nonhomogeneous Markov chain. From Lemma, if the initial d-step transition matrix is C-strong ergodicity to a constant stochastic matrix T1, the d-step transition matrix at any time is C-strong ergodicity to a constant stochastic matrix which can be given by T1 and transition matrices. The C-strong ergodicity of nonhomogeneous circular Markov chain was theoretically discussed according to the C-strong ergodicity of d-step transition matrix.
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Received: 02 July 2012
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