Multiplicative ergodicity and large deviations for an irreducible Markov chain

The paper examines multiplicative ergodic theorems and the related multipli cative Poisson equation for an irreducible Markov chain on a countable stat e 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. (i) The mean normalized products converge geometrically quickly to a finite limiting value. (ii) The multiplicative Poisson equation admits a solution. (iii) Large deviation bounds are obtainable for the empirical measures. (C) 2000 Elsevier Science B.V. All rights reserved.