OCCUPATION TIME LARGE DEVIATIONS FOR CRITICAL, BRANCHING BROWNIAN-MOTION, SUPER-BROWNIAN MOTION AND RELATED PROCESSES

We derive a large deviation principle for the occupation time function al, acting on functions with zero Lebesgue integral, for both super-Br ownian motion and critical branching Brownian motion in three dimensio ns. Our technique, based on a moment formula of Dynkin, allows us to c ompute the exact rate functions, which differ for the two processes. O btaining the exact rate function for the super-Brownian motion solves a conjecture of Lee and Remillard. We also show the corresponding CLT and obtain similar results for the superprocesses and critical branchi ng process built over the symmetric stable process of index beta in R- d, with d < 2 beta < 2 + d.