Geodesic
Fluctuation limit theorems for age-dependent critical binary branching systems
José Alfredo López-Mimbela1 ; Antonio Murillo-Salas1
1 Área de Probabilidad y Estadística, Centro de Investigación en Matemáticas, Guanajuato 36000, Mexico Mexico.
ESAIM. Proceedings, Tome 31 (2011), pp. 55-72.

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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.
DOI : 10.1051/proc/2011004

José Alfredo López-Mimbela 1 ; Antonio Murillo-Salas 1

1 Área de Probabilidad y Estadística, Centro de Investigación en Matemáticas, Guanajuato 36000, Mexico Mexico. 
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José Alfredo López-Mimbela; Antonio Murillo-Salas. Fluctuation limit theorems for age-dependent critical binary branching systems. ESAIM. Proceedings, Tome 31 (2011), pp. 55-72. doi : 10.1051/proc/2011004. http://geodesic.mathdoc.fr/articles/10.1051/proc/2011004/

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