Large deviation of diffusion processes with discontinuous drift and their occupation times

where b is smooth except possibly along the hyperplane x(1) = 0, we shall c onsider the large deviation principle for the law of the solution diffusion process and its occupation time as epsilon --> 0. In other words, we consi der P(\\X-epsilon - phi\\ < delta, \\u(epsilon) - psi\\ < delta) where u(ep silon)(t) and psi(t) are the occupation times of XE and cp in the positive half space {x epsilon R-d: x(1) > 0}, respectively. As a consequence, an un ified approach of the lower level large deviation principle for the law of X-epsilon(.) can be obtained.