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May 2013 A Lamperti-type representation of continuous-state branching processes with immigration
M. Emilia Caballero, José Luis Pérez Garmendia, Gerónimo Uribe Bravo
Ann. Probab. 41(3A): 1585-1627 (May 2013). DOI: 10.1214/12-AOP766

Abstract

Guided by the relationship between the breadth-first walk of a rooted tree and its sequence of generation sizes, we are able to include immigration in the Lamperti representation of continuous-state branching processes. We provide a representation of continuous-state branching processes with immigration by solving a random ordinary differential equation driven by a pair of independent Lévy processes. Stability of the solutions is studied and gives, in particular, limit theorems (of a type previously studied by Grimvall, Kawazu and Watanabe and by Li) and a simulation scheme for continuous-state branching processes with immigration. We further apply our stability analysis to extend Pitman’s limit theorem concerning Galton–Watson processes conditioned on total population size to more general offspring laws.

Citation

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M. Emilia Caballero. José Luis Pérez Garmendia. Gerónimo Uribe Bravo. "A Lamperti-type representation of continuous-state branching processes with immigration." Ann. Probab. 41 (3A) 1585 - 1627, May 2013. https://doi.org/10.1214/12-AOP766

Information

Published: May 2013
First available in Project Euclid: 29 April 2013

zbMATH: 1300.60101
MathSciNet: MR3098685
Digital Object Identifier: 10.1214/12-AOP766

Subjects:
Primary: 60F17, 60J80

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 3A • May 2013
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