Geodesic
A Stochastic Calculus Approach for the Brownian Snake
Canadian journal of mathematics, Tome 52 (2000) no. 1, pp. 92-118

Voir la notice de l'article provenant de la source Cambridge University Press

We 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.
DOI : 10.4153/CJM-2000-004-3
Mots-clés : 60J25, 60G44, 60J80, 60J60 
Dhersin, Jean-Stéphane; Serlet, Laurent. A Stochastic Calculus Approach for the Brownian Snake. Canadian journal of mathematics, Tome 52 (2000) no. 1, pp. 92-118. doi: 10.4153/CJM-2000-004-3
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