A SCHILDER TYPE THEOREM FOR SUPER-BROWNIAN MOTION

Let X be a d-dimensional continuous super-Brownian motion with branchi ng rate epsilon, which might be described symbolically by the ''stocha stic equation'' dX(t) = DeltaX(t)dt + root 2 epsilon X(t)dW(t) with d W(t)/dt a space-time white noise. A Schilder type theorem is establish ed concerning large deviation probabilities of X on path space as epsi lon --> 0, with a representation of the rate functional via an L(2)-fu nctional on a generalized ''Cameron-Martin space'' of measure-valued p aths.