Large Deviations For Unbounded Additive Functionals Of Markov Process With Discrete Time (non compact case)

. We combine the Donsker and Varadhan large deviation principle (l.d.p.) for the occupation measure of Markov process with certain results of Deuschel and Strook to obtain the l.d.p. for unbounded functionals. Our approach relies on the concept of exponential tightness and the Puhalskii theorem. Three illustrative examples are considered. Key words: Exponential tightness, Large deviations 1. Introduction and main result 1. Consider an ergodic Markov process ¸ = (¸ k ) k0 having R as its state space, 0 (dx) as the distribution of the initial point ¸ 0 , and = (dx) as the invariant measure. The transition probability ß(x; dy) is assumed to satisfy the Feller condition. From application point of view it is interesting to get the large deviations for functionals of the type ( 1 n P n\Gamma1 k=0 g(¸ k ); n 1) with a continuous unbounded function g = g(x). There exist different ways of solving this problem (see Gartner [8], Dueschel and Stroock [3], Veretennikov [13], Acosta [1], Elli..