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

This work concerns 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 funtional in terms of the optimal value of a minimization problem on the Euclidean space whose dimension equals the number of states.