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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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|
|Additional Information:||Copyright of this article belongs to Elseveir Science.|
|Keywords:||Markov chain; Ergodic theory; Harmonic functions; Large deviations|
|Date Deposited:||03 Nov 2009 07:19|
|Last Modified:||19 Sep 2010 04:59|
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