Fluctuation limit theorems for age-dependent critical binary branching systems

López-Mimbela, José Alfredo, and Murillo-Salas, Antonio. Emilia Caballero, Ma., et al, eds. "Fluctuation limit theorems for age-dependent critical binary branching systems." ESAIM: Proceedings 31 (2011): 55-72. <http://eudml.org/doc/251278>.

@article{López2011,
abstract = {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.},
author = {López-Mimbela, José Alfredo, Murillo-Salas, Antonio},
editor = {Emilia Caballero, Ma., Chaumont, Loïc, Hernández-Hernández, Daniel, Rivero, Víctor},
journal = {ESAIM: Proceedings},
keywords = {age-dependent branching particle system; central limit theorem; strong law of large numbers},
language = {eng},
month = {3},
pages = {55-72},
publisher = {EDP Sciences},
title = {Fluctuation limit theorems for age-dependent critical binary branching systems},
url = {http://eudml.org/doc/251278},
volume = {31},
year = {2011},
}

TY - JOUR
AU - López-Mimbela, José Alfredo
AU - Murillo-Salas, Antonio
AU - Emilia Caballero, Ma.
AU - Chaumont, Loïc
AU - Hernández-Hernández, Daniel
AU - Rivero, Víctor
TI - Fluctuation limit theorems for age-dependent critical binary branching systems
JO - ESAIM: Proceedings
DA - 2011/3//
PB - EDP Sciences
VL - 31
SP - 55
EP - 72
AB - 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.
LA - eng
KW - age-dependent branching particle system; central limit theorem; strong law of large numbers
UR - http://eudml.org/doc/251278
ER -