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October 1998 Branching processes in Lévy processes: Laplace functionals of snakes and superprocesses
Jean-François Le Gall, Yves Le Jan
Ann. Probab. 26(4): 1407-1432 (October 1998). DOI: 10.1214/aop/1022855868


We use the exploration process introduced in a previous work to develop a new construction of superprocesses with a general branching mechanism. This construction depends on a path-valued process called the Lévy snake, which is of independent interest. Our method of proof involves a calculation of the Laplace functional of the occupation field of the Lévy snake. This calculation relies on an evaluation of the corresponding moment functionals, which requires precise information about the underlying genealogical structure.


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Jean-François Le Gall. Yves Le Jan. "Branching processes in Lévy processes: Laplace functionals of snakes and superprocesses." Ann. Probab. 26 (4) 1407 - 1432, October 1998.


Published: October 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0945.60090
MathSciNet: MR1675019
Digital Object Identifier: 10.1214/aop/1022855868

Primary: 60J80
Secondary: 60G57 , 60J30

Keywords: branching process , Exploration process , Laplace functionals , Lévy process , Lévy snake , moment functionals , Superprocess

Rights: Copyright © 1998 Institute of Mathematical Statistics

Vol.26 • No. 4 • October 1998
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