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A Lemma on Super-Brownian Motion with Some Applications

  • Jean-François Le Gall
Part of the Progress in Probability book series (PRPR, volume 34)

Abstract

We prove a lemma concerning the behavior of the historical paths of super-Brownian motion near their endpoint. We use this lemma to estimate the hitting probability of a small disk for two-dimensional super-Brownian motion, thus complementing results due to Dawson, Iscoe and Perkins [3] in higher dimensions. These estimates are related to the large time behavior of the solutions of a semilinear parabolic equation, which has been investigated by several authors using analytic methods.

Keywords

Brownian Motion Strong Markov Property Positive Excursion Historical Path Trivial Path 
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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Jean-François Le Gall
    • 1
  1. 1.Laboratoire de ProbabilitésUniversité Pierre et Marie Curie 4Paris Cedex 05France

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