Treffer: Uniformly weakly ergodic classes

Summary: In [Stud. Cercet. Mat. 50, 409-415 (1998)] we defined the notion of a weakly ergodic class of a Markov chain. The notion was used to study the asymptotic behaviour and classification of the states of a nonhomogeneous Markov chain [see also our works in Math. Rep. 1(51), 117-221 (1999) and Rev. Roum. Math. Pures Appl. 45, 409-415 (2000)]. Here we define the notion of a uniformly weakly ergodic class of a Markov chain and show a generalization of a theorem of \textit{M.~Iosifescu} [``Finite Markov processes and their applications'' (1980; Zbl 0436.60001) or Rev. Roum. Math. Pures Appl. 11, 325-330 (1966; Zbl 0149.13303)] and a generalization of a theorem of Sarymsakov and Mustafin [see the above cited book of \textit{M. Iosifescu} or the paper of \textit{T. A. Sarymsakov} and \textit{H. A. Mustafin}, Trudy Sredneaziatskogo Gosuniv. 74, Fiz.-Mat. Nauki 15, 1-38 (1957)]. We also define the notion of a uniformly weakly ergodic classifier.