The Annals of Probability

Stable Hydrodynamic Limit Fluctuations of a Critical Branching Particle System in a Random Medium

Donald A. Dawson, Klaus Fleischmann, and Luis G. Gorostiza

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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.

Article information

Source
Ann. Probab., Volume 17, Number 3 (1989), 1083-1117.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991258

Digital Object Identifier
doi:10.1214/aop/1176991258

Mathematical Reviews number (MathSciNet)
MR1009446

Zentralblatt MATH identifier
0694.60078

JSTOR
links.jstor.org

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F17: Functional limit theorems; invariance principles 60G20: Generalized stochastic processes 60G55: Point processes

Keywords
Critical branching random medium (environment) fluctuations hydrodynamics stable distribution averaging infinite particle system

Citation

Dawson, Donald A.; Fleischmann, Klaus; Gorostiza, Luis G. Stable Hydrodynamic Limit Fluctuations of a Critical Branching Particle System in a Random Medium. Ann. Probab. 17 (1989), no. 3, 1083--1117. doi:10.1214/aop/1176991258. https://projecteuclid.org/euclid.aop/1176991258


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