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Locally contracting iterated functions and stability of Markov chains.

Jarner, S. F. and Tweedie, R. L. (2001) Locally contracting iterated functions and stability of Markov chains. Journal of Applied Probability, 38 (2). pp. 494-507.

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Abstract

We consider Markov chains in the context of iterated random functions and show the existence and uniqueness of an invariant distribution under a local contraction condition combined with a drift condition, extending results of Diaconis and Freedman. From these we deduce various other topological stability properties of the chains. Our conditions are typically satisfied by, for example, queueing and storage models where the global Lipschitz condition used by Diaconis and Freedman normally fails.

Item Type: Article
Journal or Publication Title: Journal of Applied Probability
Uncontrolled Keywords: Markov chains ; iterated functions ; geometric convergence ; stochastic monotonicity ; rates of convergence
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 19315
Deposited By: ep_ss_importer
Deposited On: 21 Nov 2008 11:25
Refereed?: Yes
Published?: Published
Last Modified: 26 Jul 2012 15:28
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/19315

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