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Extinction probability for single-birth chains in Markovian environments. (Chinese. English summary) Zbl 1274.60230
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