Non-degenerate conditionings of the exit measures of super-Brownian motion

Abstract

We introduce several martingale changes of measure of the law of the exit measure of super Brownian motion. These changes of measure include and generalize one arising by conditioning the exit measures to charge a point on the boun dary of a 2-dimensional domain. In the case we discuss this is a non-degenerate conditioning. We give characterizations of the new processes in terms of "immortal particle" branching processes with immigration of mass, and give application s to the study of solutions to Lu = cu^2 in D. The representations are related to those in an earlier paper, which treated the case of degenerate conditionings.