On Changes of Measure for Super Brownian Motion

Let (eta)be a superprocess under the measure P. We show the existence of probability measures which are absolutely continuous with respect to P, and whose Randon–Nikodym derivatives are suitably normalized functions of the self intersection local time of (eta). These measures correspond to measure valued processes exhibiting a certain amount of (reinforcing) self interaction in terms of both the particle motion and the branching mechanism.