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

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

2008-02-19

arxiv.org/abs/0802.2693v2

Probability Surveys 6 (2009) 62-89

Mathematics

Probability

Scientific paper

10.1214/09-PS154

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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