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Proof(s) of the Lamperti representation of continuous-state branching processes
Ma. Emilia Caballero, Amaury Lambert, and Gerónimo Uribe Bravo
Source: Probab. Surveys Volume 6
(2009), 62-89.
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.
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Keywords: Continuous-state branching processes; spectrally positive Lévy processes; random time change; stochastic integral equations; Skorohod topology
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Permanent link to this document: http://projecteuclid.org/euclid.ps/1259677176
Digital Object Identifier: doi:10.1214/09-PS154
Zentralblatt MATH identifier: 05728613
Mathematical Reviews number (MathSciNet): MR2592395
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