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

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.
Type de document :
Pré-publication, Document de travail
2009
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https://hal.archives-ouvertes.fr/hal-00257619
Contributeur : Amaury Lambert <>
Soumis le : mardi 15 septembre 2009 - 09:26:40
Dernière modification le : lundi 29 mai 2017 - 14:25:37
Document(s) archivé(s) le : mercredi 22 septembre 2010 - 13:08:33

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LampertiRepCSBP.pdf
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  • HAL Id : hal-00257619, version 2
  • ARXIV : 0802.2693

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INSMI | UPMC | USPC | PMA

Citation

Maria-Emilia Caballero, Amaury Lambert, Geronimo Uribe Bravo. Proof(s) of the Lamperti representation of Continuous-State Branching Processes. 2009. <hal-00257619v2>

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