Branching processes in Lévy processes: Laplace functionals of snakes and superprocesses
type: Item
instance of: scholarly article
title: Branching processes in Lévy processes: Laplace functionals of snakes and superprocesses
zbMATH Open document ID: 0945.60090
author: Yves Le Jan
author: J.-F. Le Gall
published in: The Annals of Probability
publication date: 2000-10-12T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60G57
zbMATH DE Number: 1355204
zbMATH Keywords: superprocesses
zbMATH Keywords: general branching mechanism
zbMATH Keywords: Lévy snake
zbMATH Keywords: occupation field
zbMATH Keywords: moment functionals
reviewed by: Luis G. Gorostiza
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1022855868
OpenAlex ID: W1575670275
cites work: Q4888858
cites work: Fluctuation theory in continuous time
cites work: Historical processes
cites work: Branching particle systems and superprocesses
cites work: Superprocesses and partial differential equations
cites work: An Introduction to Branching Measure-Valued Processes
cites work: A class of path-valued Markov processes and its applications to superprocesses
cites work: The uniform random tree in a Brownian excursion
cites work: The Brownian snake and solutions of \(\Delta u = u^ 2\) in a domain
cites work: Q4861335
cites work: Branching processes in Lévy processes: The exploration process
cites work: Superprocesses and projective limits of branching Markov process
cites work: Q3994776
cites work: Q5509983
DOI: 10.1214/AOP/1022855868
description: scientific article; zbMATH DE number 1355204