On the mixing property and the ergodic principle for nonhomogeneous Markov chains. (English) Zbl 1213.60120
The author is concerned with mixing and ergodicity of denumerable inhomogeneous Markov chains. It is shown that the collection of mixing Markov chains is not dense in norm operator topology, but a weaker property, namely, norm almost mixing (equivalent to weak ergodicity) holds in both norm and strong operator topologies.The author also generalizes and corrects some results from N. Ganikhodjaev, H. Akin and F. Mukhamedanov [Linear Algebra Appl. 416, No. 2-3, 730–741 (2006; Zbl 1096.60038)].
Reviewer: Marius Iosifescu (Bucureşti)
MSC:
| 60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |
| 15B51 | Stochastic matrices |
| 47A35 | Ergodic theory of linear operators |
Citations:
Zbl 1096.60038References:
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