On weak lumpability of denumerable Markov chains
The paper extends the results of \textit{G. Rubino} and \textit{B. Sericola} [J. Appl. Probab. 26, No. 3, 446-457 (1989; Zbl 0689.60065), Stochastic Processes Appl. 38, No. 2, 195-204 (1991; Zbl 0741.60065) and ibid. 45, No. 1, 115-125 (1993; Zbl 0764.60076)] and the author, \textit{G. Rubino} and \textit{B. Sericola} [J. Appl. Probab. 31, No. 3, 626-634 (1994; Zbl 0812.60055)] on weak lumpability of Markov chains with finite state space to denumerable Markov chains (with discrete or continuous time parameter). The problem: For a given homogeneous Markov chain the set of all initial distributions, which lead to an aggregated Markov chain with respect to a partition of the state space, is to find. In case that this set is not empty and an invariant or a quasistationary distribution exists, explicit descriptions of the aggregated Markov chain are derived.
scientific article; zbMATH DE number 844752