1. CJM 2000 (vol 52 pp. 92)
|A Stochastic Calculus Approach for the Brownian Snake |
We study the ``Brownian snake'' introduced by Le Gall, and also studied by Dynkin, Kuznetsov, Watanabe. We prove that It\^o'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.
Categories:60J25, 60G44, 60J80, 60J60