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On the conditioned exit measures of super-Brownian motion

Research paper by Thomas S. Salisbury, John Verzani

Indexed on: 31 Mar '98Published on: 31 Mar '98Published in: Mathematics - Probability



Abstract

In this paper we present a martingale related to the exit measures of super-Brownian motion. By changing measure with this martingale in the canonical way we have a new process associated with the conditioned exit measure. This measure is shown to be identical to a measure generated by a non-homogeneous branching particle system with immigration of mass. An application is given to the problem of conditioning the exit measure to hit a number of specified points on the boundary of a domain. The results are similar in flavor to the "immortal particle" picture of conditioned super-Brownian motion but more general, as the change of measure is given by a martingale which need not arise from a single harmonic function.