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Ergodicity of quasi-birth and death processes. I. (English) Zbl 1113.93103
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.

93E15Stochastic stability
60J10Markov chains (discrete-time Markov processes on discrete state spaces)
Full Text: DOI
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