Uniform stability and weak ergodicity of nonhomogeneous Markov chains defined on ordered Banach spaces with a base

Uniform stability and weak ergodicity of nonhomogeneous Markov chains defined on ordered Banach spaces with a base

In the present paper, we define an ergodicity coefficient of a positive mapping defined on ordered Banach space with a base , and study its properties. The defined coefficient is a generalization of the well-known the Dobrushin’s ergodicity coefficient. By means of the ergodicity coefficient we prov...

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Bibliographic Details
Main Author: Mukhamedov, Farrukh
Format: Article
Language:English
English
Published: Springer International Publishing 2016
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/49815/
http://irep.iium.edu.my/49815/
http://irep.iium.edu.my/49815/
http://irep.iium.edu.my/49815/1/mf-positivity-2016.pdf
http://irep.iium.edu.my/49815/4/49815_Uniform%20stability%20and%20weak%20ergodicity%20of%20nonhomogeneous%20Markov%20chains_Scopus.pdf
id iium-49815
recordtype eprints
spelling iium-498152017-04-05T07:19:29Z http://irep.iium.edu.my/49815/ Uniform stability and weak ergodicity of nonhomogeneous Markov chains defined on ordered Banach spaces with a base Mukhamedov, Farrukh QA Mathematics In the present paper, we define an ergodicity coefficient of a positive mapping defined on ordered Banach space with a base , and study its properties. The defined coefficient is a generalization of the well-known the Dobrushin’s ergodicity coefficient. By means of the ergodicity coefficient we provide uniform asymptotical stability conditions for nonhomogeneous discrete Markov chains (NDMC). These results are even new in case of von Neumann algebras. Moreover, we find necessary and sufficient conditions for the weak ergodicity of NDMC. Certain relations between uniform asymptotical stability and weak ergodicity are considered. Springer International Publishing 2016-03 Article PeerReviewed application/pdf en http://irep.iium.edu.my/49815/1/mf-positivity-2016.pdf application/pdf en http://irep.iium.edu.my/49815/4/49815_Uniform%20stability%20and%20weak%20ergodicity%20of%20nonhomogeneous%20Markov%20chains_Scopus.pdf Mukhamedov, Farrukh (2016) Uniform stability and weak ergodicity of nonhomogeneous Markov chains defined on ordered Banach spaces with a base. Positivity, 20 (1). pp. 135-153. ISSN 1385-1292 E-ISSN 1572-9281 http://link.springer.com/article/10.1007%2Fs11117-015-0346-4 10.1007/s11117-015-0346-4
repository_type Digital Repository
institution_category Local University
institution International Islamic University Malaysia
building IIUM Repository
collection Online Access
language English
English
topic QA Mathematics
spellingShingle QA Mathematics
Mukhamedov, Farrukh
Uniform stability and weak ergodicity of nonhomogeneous Markov chains defined on ordered Banach spaces with a base
description In the present paper, we define an ergodicity coefficient of a positive mapping defined on ordered Banach space with a base , and study its properties. The defined coefficient is a generalization of the well-known the Dobrushin’s ergodicity coefficient. By means of the ergodicity coefficient we provide uniform asymptotical stability conditions for nonhomogeneous discrete Markov chains (NDMC). These results are even new in case of von Neumann algebras. Moreover, we find necessary and sufficient conditions for the weak ergodicity of NDMC. Certain relations between uniform asymptotical stability and weak ergodicity are considered.
format Article
author Mukhamedov, Farrukh
author_facet Mukhamedov, Farrukh
author_sort Mukhamedov, Farrukh
title Uniform stability and weak ergodicity of nonhomogeneous Markov chains defined on ordered Banach spaces with a base
title_short Uniform stability and weak ergodicity of nonhomogeneous Markov chains defined on ordered Banach spaces with a base
title_full Uniform stability and weak ergodicity of nonhomogeneous Markov chains defined on ordered Banach spaces with a base
title_fullStr Uniform stability and weak ergodicity of nonhomogeneous Markov chains defined on ordered Banach spaces with a base
title_full_unstemmed Uniform stability and weak ergodicity of nonhomogeneous Markov chains defined on ordered Banach spaces with a base
title_sort uniform stability and weak ergodicity of nonhomogeneous markov chains defined on ordered banach spaces with a base
publisher Springer International Publishing
publishDate 2016
url http://irep.iium.edu.my/49815/
http://irep.iium.edu.my/49815/
http://irep.iium.edu.my/49815/
http://irep.iium.edu.my/49815/1/mf-positivity-2016.pdf
http://irep.iium.edu.my/49815/4/49815_Uniform%20stability%20and%20weak%20ergodicity%20of%20nonhomogeneous%20Markov%20chains_Scopus.pdf
first_indexed 2023-09-18T21:10:22Z
last_indexed 2023-09-18T21:10:22Z
_version_ 1777411212055674880

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