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Search: MSC category 60J80 ( Branching processes (Galton-Watson, birth-and-death, etc.) )

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1. CJM 2000 (vol 52 pp. 92)

Dhersin, Jean-Stéphane; Serlet, Laurent
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

2. CJM 1997 (vol 49 pp. 24)

Bertoin, Jean; Le Gall, Jean-François; Le Jan, Yves
Spatial branching processes and subordination
We present a subordination theory for spatial branching processes. This theory is developed in three different settings, first for branching Markov processes, then for superprocesses and finally for the path-valued process called the {\it Brownian snake}. As a common feature of these three situations, subordination can be used to generate new branching mechanisms. As an application, we investigate the compact support property for superprocesses with a general branching mechanism.

Categories:60J80, 60J25, 60J27, 60J55, 60G57

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