A Lamperti-type representation of continuous-state branching processes with immigration
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M. Emilia Caballero [1] ; José Luis Pérez Garmendia [2] ; Gerónimo Uribe Bravo [1]
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[1] Universidad Nacional Autónoma de México
Universidad Nacional Autónoma de México
México
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[2] University of Bath
University of Bath
Reino Unido
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- Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 3, 1, 2013, págs. 1585-1627
- Idioma: inglés
- DOI: 10.1214/12-AOP766
- Texto completo no disponible (Saber más ...)
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Resumen
Guided by the relationship between the breadth-first walk of a rooted tree and its sequence of generation sizes, we are able to include immigration in the Lamperti representation of continuous-state branching processes. We provide a representation of continuous-state branching processes with immigration by solving a random ordinary differential equation driven by a pair of independent Lévy processes. Stability of the solutions is studied and gives, in particular, limit theorems (of a type previously studied by Grimvall, Kawazu and Watanabe and by Li) and a simulation scheme for continuous-state branching processes with immigration. We further apply our stability analysis to extend Pitman’s limit theorem concerning Galton–Watson processes conditioned on total population size to more general offspring laws.
