Open Access
August, 1992 Fluctuations in a Nonlinear Reaction-Diffusion Model
Peter Kotelenez
Ann. Appl. Probab. 2(3): 669-694 (August, 1992). DOI: 10.1214/aoap/1177005654


A law of large numbers and a central limit theorem are proved for a locally interacting particle system. This system describes a chemical reaction with diffusion with linear creation and quadratic annihilation of particles. The deterministic limit is the solution of a nonlinear reaction-diffusion equation defined on an $n$-dimensional unit cube. The law of large numbers holds for any dimension $n$ and arbitrary times, whereas the central limit theorem holds only for dimension $n \leq 3$ and on a certain bounded time interval (depending on the initial distribution and on the creation rate). A propagation of chaos expansion of the correlation functions is used.


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Peter Kotelenez. "Fluctuations in a Nonlinear Reaction-Diffusion Model." Ann. Appl. Probab. 2 (3) 669 - 694, August, 1992.


Published: August, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0758.60108
MathSciNet: MR1177904
Digital Object Identifier: 10.1214/aoap/1177005654

Primary: 60K35
Secondary: 35K55 , 60F17 , 60G57 , 60H15 , 60J70

Keywords: BBGKY hierearchy , Gaussian limit , locally interacting particle system , Nonlinear reaction-diffusion equation , propagation of chaos , spatially inhomogeneous population growth , stochastic evolution equations , thermodynamic limit , van Kampen's approximation

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.2 • No. 3 • August, 1992
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