Proof(s) of the Lamperti representation of Continuous-State Branching Processes
Probability
2011-03-04 v2
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.
Keywords
Cite
@article{arxiv.0802.2693,
title = {Proof(s) of the Lamperti representation of Continuous-State Branching Processes},
author = {Maria-Emilia Caballero and Amaury Lambert and Geronimo Uribe Bravo},
journal= {arXiv preprint arXiv:0802.2693},
year = {2011}
}