LARGE DEVIATION PROBABILITIES FOR SOME RESCALED SUPERPROCESSES

We consider a class of rescaled superprocesses and derive a full large deviation principle with a ''good'' convex rate functional defined on the measure state space. The rate functional is identified as the Leg endre transform of a log-Laplace functional. The latter is described b y solutions of an explosive reaction-diffusion equation (cumulant equa tion) which is discussed in some detail. In the special case that the motion component in the model is suppressed, the variational problem i s explicitly solved showing in particular that as a rule the rate func tional is not strongly convex and not continuous.