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July, 1989 Stable Hydrodynamic Limit Fluctuations of a Critical Branching Particle System in a Random Medium
Donald A. Dawson, Klaus Fleischmann, Luis G. Gorostiza
Ann. Probab. 17(3): 1083-1117 (July, 1989). DOI: 10.1214/aop/1176991258

Abstract

A particle system in Euclidean space is considered where the particles are subject to spatial motion according to a symmetric stable law and to a critical branching law in the domain of attraction of a stable law. The "branching intensity" may be position-dependent (varying medium) or be given by a realization of a random field (random medium). It is shown that under natural assumptions the hydrodynamic limit fluctuations around the macroscopic flow are the same as those given by the "averaged medium," the limit being a generalized stable Ornstein-Uhlenbeck process. The convergence proof is based on an analysis of a nonlinear integral equation with random coefficients.

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Donald A. Dawson. Klaus Fleischmann. Luis G. Gorostiza. "Stable Hydrodynamic Limit Fluctuations of a Critical Branching Particle System in a Random Medium." Ann. Probab. 17 (3) 1083 - 1117, July, 1989. https://doi.org/10.1214/aop/1176991258

Information

Published: July, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0694.60078
MathSciNet: MR1009446
Digital Object Identifier: 10.1214/aop/1176991258

Subjects:
Primary: 60J80
Secondary: 60F17 , 60G20 , 60G55

Keywords: averaging , critical branching , Fluctuations , hydrodynamics , Infinite particle system , random medium (environment) , stable distribution

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 3 • July, 1989
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