A large deviation result for a class of Dirichlet processes

Abstract

Let λ>0 be a constant and let λ−1 <q(x) < λ be a bounded measurable function. We consider the large deviation problem for the diffusion process with generator We are going to prove that its density function satisfies $$\mathop {\lim }\limits_{t \to 0} t\log H(y,t,x) = - \frac{{\left| {x - y} \right|^2 }}{2}$$