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Pré-Publication, Document De Travail Année : 2008

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

Résumé

The representation of continuous-state branching processes (CSBPs) as time-changed Lévy processes with no negative jumps was discovered by John Lamperti in 1967 but was never proved. The goal of this paper is to provide a proof, and we actually provide two. The first one relies on studying the time-change, using martingales and the Lévy-Itô representation of Lévy processes. It gives insight into a stochastic differential equation satisfied by CSBPs and on its relevance to the branching property. The other method studies the time-change in a discrete model, where an analogous Lamperti representation is evident, and provides functional approximations to Lamperti transforms by introducing a new topology on Skorohod space. Some classical arguments used to study CSBPs are reconsidered and simplified.
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Dates et versions

hal-00257619 , version 1 (19-02-2008)
hal-00257619 , version 2 (15-09-2009)

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Maria-Emilia Caballero, Amaury Lambert, Geronimo Uribe Bravo. Proof(s) of the Lamperti representation of Continuous-State Branching Processes. 2008. ⟨hal-00257619v1⟩
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