Hu, Yangli; Yang, Xiangqun; Wang, Suming; Li, Yingqiu Extinction probability for single-birth chains in Markovian environments. (Chinese. English summary) Zbl 1274.60230 Adv. Math., Beijing 41, No. 4, 463-472 (2012). Summary: By the operator \(S_\theta\), sufficient conditions for certain extinction or non-certain extinction of critical or non-critical single-birth chains in Markovian environments are obtained. An upper bound of the extinction probability is given. MSC: 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 60K37 Processes in random environments Keywords:random environment; Markovian environment; single-birth chain; extinction probability PDF BibTeX XML Cite \textit{Y. Hu} et al., Adv. Math., Beijing 41, No. 4, 463--472 (2012; Zbl 1274.60230)