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A contraction theorem for Markov chains on general state spaces
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
2017 (English)In: Revue Roumaine De Mathématiques Pures Et Appliquées, ISSN 0035-3965, Vol. LXII, no 2Article in journal (Refereed) Published
Abstract [en]

Let {Xn, n = 0, 1, 2, ...} denote a Markov chain on a general state space and let f be a nonnegative function. The purpose of this paper is to present conditions which will imply that f(Xn) tends to 0 a.s., as n tends to infinity. As an application we obtain a result on synchronisation for random dynamical systems. At the end of the paper, we also present a result on convergence in distribution for Markov chains on general state spaces, thereby generalising a similar result for Markov chains on compact metric spaces.

AMS 2010 Subject Classification: 60J05, 60F15, 60F05.

Place, publisher, year, edition, pages
Bucharest, Romania: Editura Academiei Romane / Publishing House of the Romanian Academy , 2017. Vol. LXII, no 2
Keyword [en]
functions of Markov chains, synchronisation, convergence in distribution, random dynamical systems, iterated function systems
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-142821OAI: oai:DiVA.org:liu-142821DiVA: diva2:1154867
Available from: 2017-11-06 Created: 2017-11-06 Last updated: 2017-11-06Bibliographically approved

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Kaijser, Thomas

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