Uniform ergodicities and perturbation bounds of Markov chains on ordered Banach spaces

37th International Conference on Quantum Probability and Related Topics

Ozcan, Nazife Erkursun^1 ; Mukhamedov, Farrukh^2

Department of Mathematics, Faculty of Science, Hacettepe University, Ankara

06800, Turkey^1

Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al Ain, Abu Dhabi

15551, United Arab Emirates^2

关键词: Ergodicity;    Ergodics;    Markov operators;    Ordered Banach spaces;    Perturbation bounds;    Perturbation theory;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/819/1/012015/pdf
DOI  :  10.1088/1742-6596/819/1/012015

来源: IOP

【 摘 要 】

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.