The functional moderate deviations for Harris recurrent Markov chains and applications

We study exponentially asymptotic behaviors for the trajectories of additive functionals of Harris Markov chains. In the main result, we establish a moderate deviation principle for a pair of additive functionals of different growth rates. Moreover, we give explicit formulas for the rate functions which exhibit a non-quadratic behavior. In particular, we achieve the functional moderate deviations in two different scales. As an application, we obtain a functional law of LIL, which leads to a variety of strong limit laws in the spirit of Strassen [Z. Wahr. Geb. 3 (1964) 211-226]. (C) 2003 Elsevier SAS. All rights reserved.