LARGE DEVIATIONS WRT QUASI-EVERY STARTING POINT FOR SYMMETRICAL RIGHT PROCESSES ON GENERAL STATE-SPACES

In the work of Donsker and Varadhan, Fukushima and Takeda and that of Deuschel and Stroock it has been shown, that the lower bound for the large deviations of the empirical distribution of an ergodic symmetric Markov process is given in terms of its Dirichlet form. We give a short proof generalizing this principle to general state spaces that include, in particular, infinite dimensional and non-metrizable examples. Our result holds w.r.t. quasi-every starting point of the Markov process. Moreover we show the corresponding weak upper bound w.r.t. quasi-every starting point.