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.
@article{1022855868,
author = {Le Gall, Jean-Fran\c cois and Le Jan, Yves},
title = {Branching processes in L\'evy processes: Laplace functionals
of snakes and superprocesses},
journal = {Ann. Probab.},
volume = {26},
number = {1},
year = {1998},
pages = { 1407-1432},
language = {en},
url = {http://dml.mathdoc.fr/item/1022855868}
}
Le Gall, Jean-François; Le Jan, Yves. Branching processes in Lévy processes: Laplace functionals
of snakes and superprocesses. Ann. Probab., Tome 26 (1998) no. 1, pp. 1407-1432. http://gdmltest.u-ga.fr/item/1022855868/