Moderate deviations for Markovian occupation times

In this paper, we establish the moderate deviations for occupation times of Markov processes under the conditions given in Darling-Kac (1957. Trans. Amer. Math. Soc. 84, 444-458). When applied to the law of the iterated logarithm, our results generalize those obtained in Marcus-Rosen (1994a. Ann. Probab. 22, 626-658; 1994b. Ann. Inst. Henri Poincaré Probab. Statist. 30, 467-499) for Lévy processes and random walks, and those obtained recently by the author (1999. Ann. Probab. 27, 1324-1346) for Harris recurrent Markov chains.