The Annals of Probability

Branching processes in Lévy processes: Laplace functionals of snakes and superprocesses

Jean-François Le Gall and Yves Le Jan

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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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Ann. Probab., Volume 26, Number 4 (1998), 1407-1432.

First available in Project Euclid: 31 May 2002

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Zentralblatt MATH identifier

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J30 60G57: Random measures

Branching process Lévy process Lévy snake superprocess exploration process Laplace functionals moment functionals


Le Gall, Jean-François; Le Jan, Yves. Branching processes in Lévy processes: Laplace functionals of snakes and superprocesses. Ann. Probab. 26 (1998), no. 4, 1407--1432. doi:10.1214/aop/1022855868.

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