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Super-Brownian motion conditioned on the total mass

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  • Serlet, Laurent

Abstract

We study the super-Brownian motion (Xt) conditioned on the total mass as the continuous limit of a system of branching trajectories which genealogical structure is a Galton-Watson tree conditioned on the number of its vertices. We characterize this process by a martingale problem and give a "snake" representation. Then we apply these results to a process that we call super-Brownian excursion. Its integral is the so-called Integrated Super-Brownian Excursion that has appeared recently as limit of several systems of statistical mechanics.

Suggested Citation

  • Serlet, Laurent, 2005. "Super-Brownian motion conditioned on the total mass," Stochastic Processes and their Applications, Elsevier, vol. 115(11), pages 1782-1804, November.
  • Handle: RePEc:eee:spapps:v:115:y:2005:i:11:p:1782-1804
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    Cited by:

    1. Serlet, Laurent, 2009. "New large deviation results for some super-Brownian processes," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1696-1724, May.

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