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arXiv · 0802.2693

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

Maria-Emilia Caballero·Amaury Lambert·Geronimo Uribe Bravo
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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 L\'evy 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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Maria-Emilia Caballero, Amaury Lambert, Geronimo Uribe Bravo. 2008-02-19. Proof(s) of the Lamperti representation of Continuous-State Branching Processes. https://doi.org/10.1214/09-ps154

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