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Fluctuations of spatial branching processes with mean-field interaction

Published online by Cambridge University Press:  01 July 2016

B. Chauvin ,
P. Olivares-Rieumont  and
A. Rouault
B. Chauvin*
Affiliation:
Université Paris VI
P. Olivares-Rieumont*
Affiliation:
Universidad La Habana
A. Rouault*
Affiliation:
Université Paris XI
*
∗Postal address: Université Paris VI, Laboratoire de Probabilités, 4, Place Jussieu, tour 56, 3 ème étage, 75230 Paris Cedex 05, France.
∗∗Postal address: Universidad La Habana, Departamento de Cybernetica y Matematica, San Lazaro y L (Vedado), La Habana, Cuba.
∗∗∗Postal address: UA-CNRS 743, Statistique Appliquée, Université Paris Sud, Mathématiques (Bat. 425) 91405 Orsay Cedex, France.
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Abstract

We consider a branching Brownian motion on starting with n particles of mass 1/n, with interactive branching dynamics. The parameters are unsealed, but depend on the present state of the measure-valued process. For this mean-field model, which is a generalization of Chauvin and Rouault (1990) and Nappo and Orlandi (1988), we prove a propagation of chaos and a fluctuation theorem in ([0, T]; W–5).

Keywords

BRANCHING BROWNIAN MOTIONPARTICLE SYSTEMSFLUCTUATIONSMEAN FIELDSOBOLEV SPACES
Type
Research Article
Information
Advances in Applied Probability , Volume 23 , Issue 4 , December 1991 , pp. 716 - 732
Copyright
Copyright © Applied Probability Trust 1991 

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