The functional moderate deviations for Harris recurrent Markov chains and applications. (Q1426660)

The authors study exponentially asymptotic behaviors for the trajectories of additive functionals of Harris Markov chains. In the main result, the authors establish a moderate deviation principle for a pair of additive functionals of different growth rates. Explicit formulas for the rate functions which exhibit a non-quadratic behavior are also given. In particular, the authors achieve the functional moderate deviations in two different scales. As an application, a functional law of LIL is presented, which leads to a variety of strong limit laws in the spirit of Strassen.