van Doorn, Erik A.; Schrijner, Pauline Geometric ergodicity and quasi-stationarity in discrete-time birth-death processes. (English) Zbl 0856.60080 J. Aust. Math. Soc., Ser. B 37, No. 2, 121-144 (1995). The authors analyze the discrete-time counterpart of the first author [Adv. Appl. Probab. 17, 514-530 (1985; Zbl 0597.60080) and ibid. 23, No. 4, 683-700 (1991; Zbl 0736.60076)] which discuss exponential ergodicity and quasi-stationarity, respectively, in continuous-time birth-death processes. They obtain bounds for the decay parameter, conditions for geometric ergodicity and expressions for quasi-stationary distributions. The analysis is based on the spectral representation for the \(n\)-step transition probabilities of a birth-death process developed by S. Karlin and J. McGregor [Ill. J. Math. 3, 66-81 (1959; Zbl 0104.11804)]. Reviewer: P.R.Parthasarathy (Madras) Cited in 17 Documents MSC: 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) Keywords:random walk; decay parameter; spectral representation; birth-death processes Citations:Zbl 0597.60080; Zbl 0736.60076; Zbl 0104.11804 PDFBibTeX XMLCite \textit{E. A. van Doorn} and \textit{P. Schrijner}, J. Aust. Math. Soc., Ser. B 37, No. 2, 121--144 (1995; Zbl 0856.60080) Full Text: DOI