Multiplicative ergodicity and large deviations for an irreducible Markov chain

Balaji, S and Meyn, SP (2000) Multiplicative ergodicity and large deviations for an irreducible Markov chain. In: Stochastic Processes and their Applications, 90 (01). pp. 123-144.

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Abstract

The paper examines multiplicative ergodic theorems and the related multiplicative Poisson equation for an irreducible Markov chain on a countable state space. The partial products are considered for a real-valued function on the state space. If the function of interest satisfies a monotone condition, or is dominated by such a function, then 1. The mean normalized products converge geometrically quickly to a finite limiting value. 2. The multiplicative Poisson equation admits a solution. 3. Large deviation bounds are obtainable for the empirical measures. Author Keywords: Markov chain; Ergodic theory; Harmonic functions; Large deviations.

Item Type:	Journal Article
Publication:	Stochastic Processes and their Applications
Publisher:	Elseveir Science
Additional Information:	Copyright of this article belongs to Elseveir Science.
Keywords:	Markov chain; Ergodic theory; Harmonic functions; Large deviations
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	03 Nov 2009 07:19
Last Modified:	15 Dec 2018 06:00
URI:	http://eprints.iisc.ac.in/id/eprint/18055

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