Multiplicative ergodicity and large deviations for an irreducible Markov chain

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.