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Zbl 1113.93103
Hou, Zhenting; Li, Xiaohua
(Hou, Zhen Ting; Li, Xiao Hua)
Ergodicity of quasi-birth and death processes. I. (English)
[J] Acta Math. Sin., Engl. Ser. 23, No. 2, 201-208 (2007). ISSN 1439-8516; ISSN 1439-7617/e

Summary: Quasi-birth and death processes with block tridiagonal matrices find many applications in various areas. Neuts gave the necessary and sufficient conditions for the ordinary ergodicity and found an expression of the stationary distribution for a class of quasi-birth and death processes. In this paper we obtain the explicit necessary and sufficient conditions for $l$-ergodicity and geometric ergodicity for the class of quasi-birth and death processes, and prove that they are not strongly ergodic.

MSC 2000:: *93E15 Stochastic stability
60J10 Markov chains with discrete parameter

Keywords: ergodicity; quasi-birth and death process; Markov chain; matrix geometric solutions

Cited in: Zbl 1134.93414

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