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.
Citation
Ma. Emilia Caballero. Amaury Lambert. Gerónimo Uribe Bravo. "Proof(s) of the Lamperti representation of continuous-state branching processes." Probab. Surveys 6 62 - 89, 2009. https://doi.org/10.1214/09-PS154
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