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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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/29715/ http://irep.iium.edu.my/29715/ http://irep.iium.edu.my/29715/1/mf-BJMA%282013%29.pdf |
| Summary: | 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. |
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