On the existence of a quasistationary measure for a Markov chain
The paper continues earlier investigations done by the authors and others. The topic relates to Markov chains on a locally compact separable metric space \(X\) each of them having a weak Fellerian transition kernel \(P\) and an absorbing set of states \(S\). The main result concerns necessary and sufficient conditions under which for such a chain a quasistationary probability distribution \(\nu\) exists (that is, \(\nu\) satisfies \(\nu(B) = \frac{\int P(x;B)\nu(dx)}{\int P(x;X\setminus S)\nu(dx)}\), \(B\) a Borel set, \(B\cap S =\emptyset\)). Further it is discussed how two different cases, the one considered by G. Høgnas (1997), the other by \textit{P. A. Ferrari, H. Kesten, S. Martinez} and \textit{D. Picco} [Ann. Probab. 23, No.~2, 501-521 (1995; Zbl 0827.60061)] are included.
scientific article; zbMATH DE number 1905987