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Laws of large numbers for mesoscopic stochastic models of reacting and diffusing particles

Reichert, Christian

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Abstract

We study the asymptotic behaviour of some mesoscopic stochastic models for systems of reacting and diffusing particles (also known as density-dependent population processes) as the number of particles goes to infinity. Our approach is related to the variational approach to solving the parabolic partial differential equations that arise as limit dynamics. We first present a result for a model that converges to a classical system of reaction-diffusion equations. In addition, we discuss two models with nonlinear diffusion that give rise to quasilinear parabolic equations in the limit.

Item Type: Preprint
Series Name: IWR-Preprints
Date Deposited: 23. May 2007 07:09
Date: 2007
Faculties / Institutes: Service facilities > Interdisciplinary Center for Scientific Computing
Subjects: 510 Mathematics
Controlled Keywords: Gesetz der großen Zahlen, Reaktionsdynamik, Stochastisches Teilchensystem
Uncontrolled Keywords: Law of large numbers , reaction-diffusion model
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