On the conditioned exit measures of super-Brownian motion
Probability
2016-11-01 v1
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.
Keywords
Cite
@article{arxiv.math/9804158,
title = {On the conditioned exit measures of super-Brownian motion},
author = {Thomas S. Salisbury and John Verzani},
journal= {arXiv preprint arXiv:math/9804158},
year = {2016}
}