Flow Decomposition and Large Deviations

We study large deviations properties related to the behavior, asεgoes to 0, of diffusion processes generated byε2L1+L2, whereL1andL2are two second-order differential operators, extending recent results of Doss and Stroock and Rabeherimanana. The main tool is the decomposition theorem for flows of stochastic differential equations proved by Bismut and Kunita. We give another application of flow decomposition in a nonlinear filtering problem.