Li, Yingqiu Transience and invariant functions for Markov chains in doubly infinite random environment. (Chinese. English summary) Zbl 1038.60072 Chin. Ann. Math., Ser. A 24, No. 4, 515-520 (2003). 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. Cited in 1 Document MSC: 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 60F05 Central limit and other weak theorems 60K37 Processes in random environments Keywords:transience; \(\pi\)-irreducibility; invariant function PDFBibTeX XMLCite \textit{Y. Li}, Chin. Ann. Math., Ser. A 24, No. 4, 515--520 (2003; Zbl 1038.60072)