Branching processes in Lévy processes: Laplace functionals of snakes and superprocesses (Q1307449)

The authors continue their work [ibid. 26, No. 1, 213-252 (1998)], where a representation of the genealogy of a general continuous-state branching process was developed in terms of functionals of a spectrally positive Lévy process. This representation is applied now to a snake-like construction of superprocesses with a general branching mechanism. The construction depends on a path-valued process called the Lévy snake, similar to the Brownian snake construction developed in Le Gall's previous work. The method of proof involves the Laplace functional of the occupation field of the Lévy snake, whose calculation relies on an evaluation of moment functionals, which requires information about the genealogical structure of the model.