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Zbl 0984.60083
Zhang, Yuhui
Strong ergodicity for single-birth processes. (English)
[J] J. Appl. Probab. 38, No.1, 270-277 (2001). ISSN 0021-9002

A single-birth process is a continuous-time, irreducible Markov chain on ${\bold Z}^{+}$ whose generator $\{q_{ij}\}$ is such that $q_{i, i+1} > 0$ and $q_{i, i+j} = 0$ for all $i\in {\bold Z}^+, j\geq 2$. It is totally stable and conservative if furthermore $-q_{ii} = \sum_{i\neq j} q_{ij} < +\infty.$ The author gives a necessary, sufficient, and explicit (in terms of $\{q_{ij}\}$ only) condition for the strong ergodicity (i.e. uniform convergence towards the stationary measure) of a totally stable conservative single-birth process. Applications to the so-called Schögl model are given.
[Thomas Simon (Berlin)]

MSC 2000:: *60J25 Markov processes with continuous parameter

Keywords: strong ergodicity; single-birth $Q$-process; Schögl model

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