Inverse problems for ergodicity of Markov chains |
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Authors: | Zhi-Feng Wei |
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Affiliation: | 1. School of Mathematical Sciences and Lab. Math. Com. Sys., Beijing Normal University, Beijing 100875, China;2. Department of Mathematics, Indiana University Bloomington, 831 E 3rd St., Bloomington, IN 47405, United States |
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Abstract: | For continuous-time Markov chains, we provide criteria for non-ergodicity, non-algebraic ergodicity, non-exponential ergodicity, and non-strong ergodicity. For discrete-time Markov chains, criteria for non-ergodicity, non-algebraic ergodicity, and non-strong ergodicity are given. Our criteria are in terms of the existence of solutions to inequalities involving the Q-matrix (or transition matrix P in time-discrete case) of the chain. Meanwhile, these practical criteria are applied to some examples, including a special class of single birth processes and several multi-dimensional models. |
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Keywords: | Markov chain Single birth processes Non-ergodicity Instability Test function |
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