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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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Main Author: Mukhamedov, Farrukh
Format: Article
Language:English
English
Published: Springer International Publishing 2016
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/49815/1/mf-positivity-2016.pdf
http://irep.iium.edu.my/49815/4/49815_Uniform%20stability%20and%20weak%20ergodicity%20of%20nonhomogeneous%20Markov%20chains_Scopus.pdf
http://irep.iium.edu.my/49815/
http://link.springer.com/article/10.1007%2Fs11117-015-0346-4
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spelling my.iium.irep.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 REM 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 http://link.springer.com/article/10.1007%2Fs11117-015-0346-4 10.1007/s11117-015-0346-4
institution Universiti Islam Antarabangsa Malaysia
building IIUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider International Islamic University Malaysia
content_source IIUM Repository (IREP)
url_provider http://irep.iium.edu.my/
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/49815/1/mf-positivity-2016.pdf
http://irep.iium.edu.my/49815/4/49815_Uniform%20stability%20and%20weak%20ergodicity%20of%20nonhomogeneous%20Markov%20chains_Scopus.pdf
http://irep.iium.edu.my/49815/
http://link.springer.com/article/10.1007%2Fs11117-015-0346-4
_version_ 1643613601570750464
score 13.244745

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