The Annals of Probability
- Ann. Probab.
- Volume 17, Number 3 (1989), 1083-1117.
Stable Hydrodynamic Limit Fluctuations of a Critical Branching Particle System in a Random Medium
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.
Ann. Probab., Volume 17, Number 3 (1989), 1083-1117.
First available in Project Euclid: 19 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F17: Functional limit theorems; invariance principles 60G20: Generalized stochastic processes 60G55: Point processes
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