LARGE DEVIATIONS WRT QUASI-EVERY STARTING POINT FOR SYMMETRICAL RIGHTPROCESSES 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 l arge deviations of the empirical distribution of an ergodic symmetric Markov process is given in terms of its Dirichlet form. We give a shor t proof generalizing this principle to general state spaces that inclu de, in particular, infinite dimensional and non-metrizable examples. O ur result holds w.r.t. quasi-every starting point of the Markov proces s. Moreover we show the corresponding weak upper bound w.r.t. quasi-ev ery starting point.