Large deviation principles for Markov processes in noncompact cases

The purpose of this thesis is to study the asymptotic distribution of time averages of certain additive functionals related to a continuous time, time homogeneous Markov process. Conditions are given for the existence of abstract rate functions satisfying the corresponding large deviation principles. These conditions are essentially intergrability conditions on the transition probability function allowing one to simultaneously treat different large deviation settings. The conditions apply to Markov processes with noncompact state space and are verified for a certain class of diffusion processes on R/sup N/. The large deviation principles obtained can be used to symptotically evaluate certain integrals arising from problems related to ergodic theory