LARGE DEVIATION PROPERTY FOR RlEMANNIAN BROWNIAN MOTION ON A COMPLETE MANIFOLD

Let M be a connected, complete Riemannian manifold with Ricci curvatuife bounded from below, p(t,x,y) be the transition density function of the Riemannian Brownian motion, and for each $\epsilon >0,(P_{\epsilon,x})$ be the diffusion measure family associated with the transition density function p(\epsilon t,x, y). In this paper, it is shown that (P_{\epsilon ,x}) has strongly large deviation properties $\epsilon \rightarrow 0$.