Remarks on ergodic conditions for Markov processes on Polish spaces. (English) Zbl 0815.60072

Stettner, Łukasz

Bull. Pol. Acad. Sci., Math. 42, No. 2, 103-114 (1994).

Three ergodic conditions for Markov processes on complete metric spaces are given. The first one provides a sufficient condition for Markov processes to be Harris and to have iterations of the transition operator convergent to the invariant measure in the variation norm. The second condition is necessary and sufficient for the existence of an invariant measure for Feller Markov processes. Finally, topological assumptions that guarantee the uniqueness of invariant measures for Feller Markov processes are shown. The studies were motivated by stochastic evolution equations in Hilbert spaces.

Reviewer: Ł.Stettner (Warszawa)

MSC:

60J25	Continuous-time Markov processes on general state spaces
60F99	Limit theorems in probability theory
60G10	Stationary stochastic processes
47A35	Ergodic theory of linear operators

Keywords:

Harris process; Polish space; ergodic conditions for Markov processes; Feller Markov processes; stochastic evolution equations