Super-Brownian motion conditioned on the total mass

Laurent Serlet

Stochastic Processes and their Applications, 2005, vol. 115, issue 11, 1782-1804

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.

Keywords: Particle; system; Martingale; problem; Galton-Watson; tree; Super-Brownian; motion; Integrated; super-Brownian; excursion (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (1)

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