Weak ergodicity of nonhomogeneous Markov chains on noncommutative L1-spaces
In this paper we study certain properties of Dobrushin's ergod- icity coe�cient for stochastic operators de�ned on noncommutative L 1 -spaces associated with semi-�nite von Neumann algebras. Such results extends the well-known classical ones to a noncommutative setting. This allows us to i...
| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Ferdowsi University of Mashhad.
2013
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| Online Access: | http://irep.iium.edu.my/29715/1/mf-BJMA%282013%29.pdf |
| _version_ | 1825647246543159296 |
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| author | Mukhamedov, Farrukh |
| author_facet | Mukhamedov, Farrukh |
| author_sort | Mukhamedov, Farrukh |
| collection | IIUM |
| description | In this paper we study certain properties of Dobrushin's ergod-
icity coe�cient for stochastic operators de�ned on noncommutative L
1
-spaces
associated with semi-�nite von Neumann algebras. Such results extends the
well-known classical ones to a noncommutative setting. This allows us to in-
vestigate the weak ergodicity of nonhomogeneous discrete Markov processes
(NDMP) by means of the ergodicity coe�cient. We provide a su�cient condi-
tions for such processes to satisfy the weak ergodicity. Moreover, a necessary
and su�cient condition is given for the satisfaction of the L
1
-weak ergodicity
of NDMP. It is also provided an example showing that L
1
-weak ergodicity is
weaker that weak ergodicity. We applied the main results to several concrete
examples of noncommutative NDMP. |
| first_indexed | 2024-03-05T23:14:48Z |
| format | Article |
| id | oai:generic.eprints.org:29715 |
| institution | International Islamic University Malaysia |
| language | English |
| last_indexed | 2024-03-05T23:14:48Z |
| publishDate | 2013 |
| publisher | Ferdowsi University of Mashhad. |
| record_format | dspace |
| spelling | oai:generic.eprints.org:297152013-04-23T07:06:01Z http://irep.iium.edu.my/29715/ Weak ergodicity of nonhomogeneous Markov chains on noncommutative L1-spaces Mukhamedov, Farrukh QA Mathematics In this paper we study certain properties of Dobrushin's ergod- icity coe�cient for stochastic operators de�ned on noncommutative L 1 -spaces associated with semi-�nite von Neumann algebras. Such results extends the well-known classical ones to a noncommutative setting. This allows us to in- vestigate the weak ergodicity of nonhomogeneous discrete Markov processes (NDMP) by means of the ergodicity coe�cient. We provide a su�cient condi- tions for such processes to satisfy the weak ergodicity. Moreover, a necessary and su�cient condition is given for the satisfaction of the L 1 -weak ergodicity of NDMP. It is also provided an example showing that L 1 -weak ergodicity is weaker that weak ergodicity. We applied the main results to several concrete examples of noncommutative NDMP. Ferdowsi University of Mashhad. 2013 Article PeerReviewed application/pdf en http://irep.iium.edu.my/29715/1/mf-BJMA%282013%29.pdf Mukhamedov, Farrukh (2013) Weak ergodicity of nonhomogeneous Markov chains on noncommutative L1-spaces. Banach Journal of Mathematical Analysis, 7 (2). pp. 53-73. ISSN 1735-8787 http://www.emis.de/journals/BJMA/ |
| spellingShingle | QA Mathematics Mukhamedov, Farrukh Weak ergodicity of nonhomogeneous Markov chains on noncommutative L1-spaces |
| title | Weak ergodicity of nonhomogeneous Markov chains on noncommutative L1-spaces |
| title_full | Weak ergodicity of nonhomogeneous Markov chains on noncommutative L1-spaces |
| title_fullStr | Weak ergodicity of nonhomogeneous Markov chains on noncommutative L1-spaces |
| title_full_unstemmed | Weak ergodicity of nonhomogeneous Markov chains on noncommutative L1-spaces |
| title_short | Weak ergodicity of nonhomogeneous Markov chains on noncommutative L1-spaces |
| title_sort | weak ergodicity of nonhomogeneous markov chains on noncommutative l1 spaces |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/29715/1/mf-BJMA%282013%29.pdf |
| work_keys_str_mv | AT mukhamedovfarrukh weakergodicityofnonhomogeneousmarkovchainsonnoncommutativel1spaces |