Exponential Changes of Measure for the Feller Diffusion and Superprocesses

摘要

Let eta be a super process under the measure P. We show the existence ofprobability measures which are absolutely continuous with respect to P, and whose Radon-Nikodym derivatives are suitably normalized exponential functions of the self intersection local time of eta. These measures correspond to measure valued processes exhibiting a certain amount of self interaction. A finite time divergence of the total mass (1, etat) is shown to occur in a related model in which the change of measure involves the occupation measure of the super process. As an independently interesting side issue we also obtain a number of results related to a self interacting version of the Feller diffusion.