# Fluctuation limit theorems for age-dependent critical binary branching systems

José Alfredo López-Mimbela; Antonio Murillo-Salas

ESAIM: Proceedings (2011)

- Volume: 31, page 55-72
- ISSN: 1270-900X

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topLópez-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 -

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