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.
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Received: 27 August 1998 / Revised version: 8 January 1999
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Salisbury, T., Verzani, J. On the conditioned exit measures of super Brownian motion. Probab Theory Relat Fields 115, 237–285 (1999). https://doi.org/10.1007/s004400050271
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DOI: https://doi.org/10.1007/s004400050271