Multiplicative ergodicity and large deviations for an irreducible Markov chain

S. Balaji and S. P. Meyn

Stochastic Processes and their Applications, 2000, vol. 90, issue 1, 123-144

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.

Keywords: Markov; chain; Ergodic; theory; Harmonic; functions; Large; deviations (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (15)

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