On the conditioned exit measures of super Brownian motion |
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Authors: | Thomas S. Salisbury John Verzani |
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Affiliation: | (1) Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J 1P3. e-mail: salt@nexus.yorku.ca, CA;(2) Department of Mathematics, CUNY – College of Staten Island, Staten Island, NY 10314, USA. e-mail: verzani@math.csi.cuny.edu, US |
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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. Received: 27 August 1998 / Revised version: 8 January 1999 |
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Keywords: | Mathematics Subject Classification (1991): Primary 60G57, 60G42 Secondary 60F99 |
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