| Issue |
ESAIM: Proc.
Volume 31, January 2011
X Symposium on Probability and Stochastic Processes and the First Joint Meeting France-Mexico of Probability
|
|
|---|---|---|
| Page(s) | 55 - 72 | |
| DOI | https://doi.org/10.1051/proc/2011004 | |
| Published online | 15 March 2011 | |
Fluctuation limit theorems for age-dependent critical binary branching systems
Área de Probabilidad y Estadística, Centro de Investigación
en Matemáticas, Guanajuato 36000, Mexico Mexico.
E-mail: jalfredo@cimat.mx, murillo@cimat.mx.
We consider an age-dependent branching particle system in ℝd, where the particles are subject to α-stable migration (0 < α ≤ 2), critical binary branching, and general (non-arithmetic) lifetimes distribution. The population starts off from a Poisson random field in ℝd with Lebesgue intensity. We prove functional central limit theorems and strong laws of large numbers under two rescalings: high particle density, and a space-time rescaling that preserves the migration distribution. Properties of the limit processes such as Markov property, almost sure continuity of paths and generalized Langevin equation, are also investigated.
© EDP Sciences, ESAIM 2011
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