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On Markov chains induced by partitioned transition probability matrices
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
2009 (English)Report (Other academic)
Abstract [en]

Let S be a denumerable state space and let P be a transition probability matrix on S. If a denumerable set M of nonnegative matrices is such that the sum of the matrices is equal to P, then we call M a partition of P.

Let K denote the set of probability vectors on S. With every partition M of P we can associate a transition probability function P M on K defined in such a way that if pK and MM are such that ‖pM‖ > 0, then, with probability ‖pM‖, the vector p is transferred to the vector pM/‖pM‖. Here ‖·‖ denotes the l 1-norm.

In this paper we investigate the convergence in distribution for Markov chains generated by transition probability functions induced by partitions of transition probability matrices. The main motivation for this investigation is the application of the convergence results obtained to filtering processes of partially observed Markov chains with denumerable state space.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2009.
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2009:07
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-19841ISRN: LiTH-MAT-R-2009/07--SEOAI: oai:DiVA.org:liu-19841DiVA: diva2:229383
Available from: 2009-08-12 Created: 2009-08-12 Last updated: 2016-07-08Bibliographically approved

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Aslo published in Acta Mathematica SinicaFull text availabla at arXiv.orgArticle published in DiVA

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Kaijser, Thomas

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