brownian snake
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2004 ◽  
Vol 128 (4) ◽  
pp. 475-516
Author(s):  
Romain Abraham ◽  
Jean-Fran�ois Delmas
Keyword(s):  

2002 ◽  
Vol 73 (3-4) ◽  
pp. 287-308 ◽  
Author(s):  
R. Abraham ◽  
L. Serlet
Keyword(s):  

2001 ◽  
Vol 29 (1) ◽  
pp. 305-316 ◽  
Author(s):  
Jean-François Delmas ◽  
Jean-Stéphane Dhersin
Keyword(s):  

2000 ◽  
Vol 52 (1) ◽  
pp. 92-118 ◽  
Author(s):  
Jean-Stéphane Dhersin ◽  
Laurent Serlet

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.


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