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On the conditioned exit measures of super Brownian motion
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  • Published: September 1999

On the conditioned exit measures of super Brownian motion

  • Thomas S. Salisbury1 &
  • John Verzani2 

Probability Theory and Related Fields volume 115, pages 237–285 (1999)Cite this article

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  • 17 Citations

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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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J 1P3. e-mail: salt@nexus.yorku.ca, , , , , , CA

    Thomas S. Salisbury

  2. Department of Mathematics, CUNY – College of Staten Island, Staten Island, NY 10314, USA. e-mail: verzani@math.csi.cuny.edu, , , , , , US

    John Verzani

Authors
  1. Thomas S. Salisbury
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  2. John Verzani
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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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  • Issue Date: September 1999

  • DOI: https://doi.org/10.1007/s004400050271

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  • Mathematics Subject Classification (1991): Primary 60G57, 60G42; Secondary 60F99
  • Key words: Exit measure – Super Brownian motion – Martingale change of measure – Immortal particle description – Conditioned limit theorems
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