Eigentime identity for transient Markov chains |
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Authors: | Yong-Hua Mao |
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Affiliation: | Department of Mathematics, Beijing Normal University, Beijing 100875, People's Republic of China |
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Abstract: | An eigentime identity is proved for transient symmetrizable Markov chains. For general Markov chains, if the trace of Green matrix is finite, then the expectation of first leap time is uniformly bounded, both of which are proved to be equivalent for single birth processes. For birth-death processes, the explicit formulas are presented. As an application, we give the bounds of exponential convergence rates of (sub-) Markov semigroup Pt from l∞ to l∞. |
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Keywords: | Markov chain Eigenvalue Essential spectrum Eigentime identity Green matrix |
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