The stopped distributions of a controlled Markov chain with discrete time (Q1064669)

A characterization is given, in terms of excessive functions, of possible stopped distributions of a controlled Markov chain with given initial distribution. Control here is understood as a mixing of a given finite number of Markov chains. It is an extension of the \textit{H. Rost} theorem [Ann. Inst. Fourier 21, 253-270 (1971; Zbl 0197.442)] for more than one Markov kernel. Similar result for continuous time in ''The stopped distributions of a controlled Markov chain with continuous time'' will appear in early 1987.)