In this paper, we study the moderate deviation principle of an inhomogeneous integral functional of a Markov process (xi (s)) which is exponentially ergodic, i.e. the moderate deviations of 1/root epsilonh(epsilon) integral (1)(0) f(s,xi (s/epsilon))ds, in the space of continuous functions from [0, 1] to R-d, where f is some R-d-valued bounded function. Our method relies on the characterization of the exponential ergodicity by Down-Meyn-Tweedie (Ann. Probab. 25(3) (1995) 1671) and the regeneration split chain technique for Markov chain. We then apply it to establish the moderate deviations of X-f(epsilon) given by the following randomly perturbed dynamic system in R-d <(X) over dot>(epsilon)(t) = b(X-t(epsilon), xi (t/epsilon)), around its limit behavior, usually called the averaging principle, studied by Freidlin and Wentzell (Random Perturbations of Dynamical Systems, Springer, New York, 1984). (C) 2001 Elsevier Science B.V. All rights reserved. [References: 28]
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