Author:
Dhersin Jean-Stéphane,Serlet Laurent
Abstract
AbstractWe study the “Brownian snake” introduced by Le Gall, and also studied by Dynkin, Kuznetsov, Watanabe. We prove that Itô’s formula holds for a wide class of functionals. As a consequence, we give a new proof of the connections between the Brownian snake and super-Brownian motion. We also give a new definition of the Brownian snake as the solution of a well-posed martingale problem. Finally, we construct a modified Brownian snake whose lifetime is driven by a path-dependent stochastic equation. This process gives a representation of some super-processes.
Publisher
Canadian Mathematical Society
Cited by
5 articles.
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1. The coalescent point process of multi-type branching trees;Stochastic Processes and their Applications;2014-12
2. A Williams decomposition for spatially dependent superprocesses;Electronic Journal of Probability;2013-01-01
3. Super Brownian motion with interactions;Stochastic Processes and their Applications;2003-10
4. Catalytic branching and the Brownian snake;Stochastic Processes and their Applications;2003-02
5. Representations of the Brownian snake with drift;Stochastics and Stochastic Reports;2002-01