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Institute of Mathematical Statistics, Probability Surveys, none(6), 2009

DOI: 10.1214/09-ps154

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Proof(s) of the Lamperti representation of Continuous-State Branching Processes

Journal article published in 2008 by Maria-Emilia Caballero, M.-A. Emilia Caballero, Amaury Lambert ORCID, M. E. Caballero, Gerónimo Uribe Bravo, Geronimo Uribe Bravo
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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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.