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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


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.


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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.


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

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

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

Vol.6 • 2009
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