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Periodic behavior of the stochastic Brusselator in the mean-field limit
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  • Published: June 1986

Periodic behavior of the stochastic Brusselator in the mean-field limit

  • Michael Scheutzow1 

Probability Theory and Related Fields volume 72, pages 425–462 (1986)Cite this article

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  • 32 Citations

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Summary

We prove a “propagation of chaos” result for the mean-field limit of a model for a trimolecular chemical reaction called “Brusselator”. Then we show that the pair of nonlinear (i.e. law-dependent) stochastic differential equations describing the evolution of the concentration of the molecules at a given site in the mean field limit has a solution with a periodic law (in t). Finally we identify the limit and establish a central limit theorem for the periodic law in the case where the noise tends to zero.

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Universität Kaiserslautern, D-6750, Kaiserslautern, Federal Republic of Germany

    Michael Scheutzow

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  1. Michael Scheutzow
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Additional information

Part of this work was performed while on leave at the Department of Mathematics and Statistics, Carleton University, Ottawa, Canada and supported by NSERC operating grants of M. Csörgö and D. Dawson

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Scheutzow, M. Periodic behavior of the stochastic Brusselator in the mean-field limit. Probab. Th. Rel. Fields 72, 425–462 (1986). https://doi.org/10.1007/BF00334195

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  • Received: 26 June 1985

  • Issue Date: June 1986

  • DOI: https://doi.org/10.1007/BF00334195

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Keywords

  • Differential Equation
  • Stochastic Process
  • Probability Theory
  • Limit Theorem
  • Statistical Theory
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