TY - JOUR
T1 - Uniform ergodicities and perturbation bounds of Markov chains on base norm spaces
AU - Erkurşun-Özcan, Nazife
AU - Mukhamedov, Farrukh
N1 - Funding Information:
Acknowledgments. The first author (N.E.) thanks the Hacettepe University Scientific Research Projects Coordination Unit for support of this project under the Project Number: 014 D12 601 005 -832. She is also grateful to the International Islamic University Malaysia for kind hospitality during her research stay where this work was started. The second author (F.M.) also thanks the Hacettepe University (Turkey) for kind hospitality during 5–9 September 2015, where a part of this work was carried out. Finally, the authors are grateful to an anonymous referee whose useful comments and suggestions improved the presentation of this paper.
Publisher Copyright:
© 2018, © 2018 NISC (Pty) Ltd.
PY - 2018/8/18
Y1 - 2018/8/18
N2 - It is known that Dobrushin's ergodicity coefficient is one of the effective tools in the investigations of limiting behavior of Markov processes. Several interesting properties of the ergodicity coefficient of a positive mapping defined on base norm spaces have been studied. In this paper, we consider uniformly mean ergodic and asymptotically stable Markov operators on such spaces. In terms of the ergodicity coefficient, we establish uniform mean ergodicity criterion. Moreover, we develop the perturbation theory for uniformly asymptotically stable Markov chains on base norm spaces. In particularly, main results open new perspectives in the perturbation theory for quantum Markov processes defined on von Neumann algebras.
AB - It is known that Dobrushin's ergodicity coefficient is one of the effective tools in the investigations of limiting behavior of Markov processes. Several interesting properties of the ergodicity coefficient of a positive mapping defined on base norm spaces have been studied. In this paper, we consider uniformly mean ergodic and asymptotically stable Markov operators on such spaces. In terms of the ergodicity coefficient, we establish uniform mean ergodicity criterion. Moreover, we develop the perturbation theory for uniformly asymptotically stable Markov chains on base norm spaces. In particularly, main results open new perspectives in the perturbation theory for quantum Markov processes defined on von Neumann algebras.
KW - Dobrushin's coefficient
KW - Markov operator
KW - Uniformly asymptotically stable
KW - base norm space
KW - perturbation bound
KW - uniformly mean ergodic
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U2 - 10.2989/16073606.2017.1415231
DO - 10.2989/16073606.2017.1415231
M3 - Article
AN - SCOPUS:85041831460
SN - 1607-3606
VL - 41
SP - 863
EP - 876
JO - Quaestiones Mathematicae
JF - Quaestiones Mathematicae
IS - 6
ER -