Principles of large deviations for the empirical processes of the Ornstein-Uhlenbeck process

The present paper deals with principles of large deviations for the empirical processes of the Omstein-Uhlenbeck process. One such principle due to Donsker and Varadhan is well known. It uses as underlying space C(R. R-d) endowed with the topology of uniform convergence on compact sets. Thr principles of large deviations proved in the present paper use as underlying spaces appropriate subspaces of C(R, R-d) endowed with weighted supremum norms. These principles are natural generalizations of the principle of Donsker and Varadhan.