Abstract
In this paper, we consider uniformly mean ergodic and uniformly asymptotical stable Markov operators on ordered Banach spaces. In terms of the ergodicity coefficient, we show the equivalence of uniform and weak mean ergodicities of Markov operators. This result allowed us to establish a category theorem for uniformly mean ergodic Markov operators. Furthermore, using properties of the ergodicity coefficient, we develop the perturbation theory for uniformly asymptotical stable Markov chains in the abstract scheme.
Highlights
It is well-known [18] that the transition probabilities P (x, A) (defined on a measurable s∫pace (E, F)) of Markov processes naturally define a linear operator by f (y)P (x, dy), which is called Markov operator and acts on the associatedT f (x) = L1-spaces.Quantum analogous of Markov processes naturally appear in various directions of quantum physics such as quantum statistical physics and quantum optics etc [1]
In terms of the ergodicity coefficient, we show the equivalence of uniform and weak mean ergodicities of Markov operators
This result allowed us to establish a category theorem for uniformly mean ergodic Markov operators
Summary
Uniform ergodicities and perturbation bounds of Markov chains on ordered Banach spaces To cite this article: Nazife Erkursun Özcan and Farrukh Mukhamedov 2017 J. View the article online for updates and enhancements. - On Dobrushin Ergodicity Coefficient and weak ergodicity of Markov Chains on Jordan Algebras Farrukh Mukhamedov. - Representing Lumped Markov Chains by Minimal Polynomials over Field GF(q) V M Zakharov, S V Shalagin and B F Eminov
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