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

By María Emilia Caballero, Amaury Lambert, Gerónimo Uribe Bravo. 2008

111 citations recorded by the source corpus.

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 Levy 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.

Subfields: Finance, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c2f4226d89f85de95104b55d03f747aa76fa4c2a

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Citations in the corpus

Stochastic Models for Structured Populations: Scaling Limits and Long Time Behavior (2015, background): “[58, 20] The càdlàg Markov processes Z which take values in [0,∞] and satisfy the branching property are in one to one correspondence with Lévy processes Y with no negative jumps, through the equation Zt = Y + ∫ t 0 Zs .”
The Theory of Scale Functions for Spectrally Negative Lévy Processes (2011, background): “[26] and Kyprianou and Pardo [72] for further computations in this spirit and Lambert [77] for further applications in population biology.”
Population Dynamics and Random Genealogies (2008, background): “In a joint work with Maria–Emilia Caballero and Gerónimo Uribe (UNAM, Mexico), we actually provide two proofs of this theorem[18].”