On a representation of Varadhan´s functional as a convex minimization problem

This work deals with Markov chains with finite state endowed with a real valued cost function. It is assumed that the Markov process has a single recurrent class, but the set of transient states is not necessarily empty. The Varadhan´s functional measures the exponential rate of growth of an aggregated cost function. The main goal of this paper is to establish a representation of this functional in terms of the optimal value of a minimization problem on the Euclidean space whose dimension equals the number of states.