2008/02/29 by Maria-Emilia Caballero, Ma.-Emilia Caballero, Amaury Lambert +2
Economics, Econometrics and Finance · Mathematics · #Markov Chains and Monte Carlo Methods #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60B10 #msc:60G44 #msc:60G51 #msc:60H20 #msc:60J80
paper · pdf · doi:10.1214/09-ps154
published as Probability Surveys 6 (2009) 62-89
openalex publication_date 2009/01/01 · arxiv created 2009/09/15 · arxiv updated 2011/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.