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Transience and invariant functions for Markov chains in doubly infinite random environment. (Chinese. English summary) Zbl 1038.60072

Summary: Investigating Markov chains in random environments, the concepts of \(\pi\)-irreducibility, recurrence and transience of Markov chains in doubly infinite random environment are introduced. A sufficient and necessary condition that \(\pi\)-irreducible Markov chains in doubly infinite random environment are transient is given. The concepts for invariant functions of Markov chains in doubly infinite random environment are introduced. Their existence and basic properties are studied. Using these properties, a criterion that \(\pi\)-irreducible Markov chains in doubly infinite random environment are transient is given.

MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60F05 Central limit and other weak theorems
60K37 Processes in random environments
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