A Schilder type theorem for super-Brownian motion

Let X be a d-dimensional continuous super-Brownian motion with branching rate epsilon, which might be described symbolically by the ''stochastic equation'' dX(t) = Delta*X(t)dt + root 2 epsilon X(t)dW(t) with dW(t)/dt a space-time white noise. A Schilder type theorem is established concerning large deviation probabilities of X on path space as epsilon --> 0, with a representation of the rate functional via an L(2)-functional on a generalized ''Cameron-Martin space'' of measure-valued paths.