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Sur la mesure de sortie du super mouvement brownien
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  • Published: June 1994

Sur la mesure de sortie du super mouvement brownien

  • Romain Abraham1 &
  • Jean-François Le Gall1 

Probability Theory and Related Fields volume 99, pages 251–275 (1994)Cite this article

Summary

We study some properties of the exit measure of super Brownian motion from a smooth domainD inR d. In particular, we give precise estimates for the probability that the exit measure gives a positive mass to a small ball on the boundary. As an application, we compute the Hausdorff dimension of the support of the exit measure. In dimension 2, we prove that the exit measure is absolutely continuous with respect to the Lebesgue measure on the boundary. In connection with Dynkin's work, our results give some information on the behavior of solutions of Δu=u 2 inD, and are related to the characterization of removable singularities at the boundary. As a consequence of our estimates, we give a sufficient condition for the uniqueness of the positive solution of Δu=u 2 inD that tends to ∞ on an open subsetO of ϖD and to 0 on the complement in ϖD of the closure ofO. Our proofs use the path-valued process studied in [L2, L3].

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Authors and Affiliations

  1. Laboratoire de Probabilités, Université Paris VI, 4, Place Jussieu, F-75252, Paris, Cedex 05

    Romain Abraham & Jean-François Le Gall

Authors
  1. Romain Abraham
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  2. Jean-François Le Gall
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Abraham, R., Le Gall, JF. Sur la mesure de sortie du super mouvement brownien. Probab. Th. Rel. Fields 99, 251–275 (1994). https://doi.org/10.1007/BF01199025

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  • Received: 20 July 1993

  • Revised: 17 November 1993

  • Issue Date: June 1994

  • DOI: https://doi.org/10.1007/BF01199025

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Mathematics Subject Classification (1991)

  • 60G57
  • 60G17
  • 60H30
  • 35J60
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