Li, Yingqiu Existence and irreducibility of Markov chains in doubly infinite random environment. (Chinese. English summary) Zbl 0990.60072 Acta Math. Sci., Ser. A, Chin. Ed. 21, No. 4, 439-442 (2001). Summary: Existence of Markov chains in a doubly infinite random environment is discussed. The concepts of irreducibility for Markov chains in a doubly infinite random environment are first introduced, their properties are discussed, and strong irreducibility is introduced. MSC: 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 60F05 Central limit and other weak theorems Keywords:doubly infinite random environment; Markov chain; \(\pi\)-irreducibility; strong \(\pi\)-irreducibility PDFBibTeX XMLCite \textit{Y. Li}, Acta Math. Sci., Ser. A, Chin. Ed. 21, No. 4, 439--442 (2001; Zbl 0990.60072)