Open Access
Translator Disclaimer
2009 Proof(s) of the Lamperti representation of continuous-state branching processes
Ma. Emilia Caballero, Amaury Lambert, Gerónimo Uribe Bravo
Probab. Surveys 6: 62-89 (2009). DOI: 10.1214/09-PS154

Abstract

This paper uses two new ingredients, namely stochastic differential equations satisfied by continuous-state branching processes (CSBPs), and a topology under which the Lamperti transformation is continuous, in order to provide self-contained proofs of Lamperti’s 1967 representation of CSBPs in terms of spectrally positive Lévy processes. The first proof is a direct probabilistic proof, and the second one uses approximations by discrete processes, for which the Lamperti representation is evident.

Citation

Download Citation

Ma. Emilia Caballero. Amaury Lambert. Gerónimo Uribe Bravo. "Proof(s) of the Lamperti representation of continuous-state branching processes." Probab. Surveys 6 62 - 89, 2009. https://doi.org/10.1214/09-PS154

Information

Published: 2009
First available in Project Euclid: 1 December 2009

zbMATH: 1194.60053
MathSciNet: MR2592395
Digital Object Identifier: 10.1214/09-PS154

Subjects:
Primary: 60J80
Secondary: 60B10 , 60G44 , 60G51 , 60H20

Keywords: continuous-state branching processes , Random time change , Skorohod topology , spectrally positive Lévy processes , stochastic integral equations

Rights: Copyright © 2009 The Institute of Mathematical Statistics and the Bernoulli Society

JOURNAL ARTICLE
28 PAGES


SHARE
Vol.6 • 2009
Back to Top