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An ergodic theorem for Schlögl models with small migration
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  • Published: March 1990

An ergodic theorem for Schlögl models with small migration

  • Claudia Neuhauser1 

Probability Theory and Related Fields volume 85, pages 27–32 (1990)Cite this article

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Summary

We consider a class of reaction-diffusion processes with state space NZd. The reaction part is described by a birth and death process where the rates are given by certain polynomials. The diffusion part is an irreducible symmetric random walk. We prove ergodicity in the case of a sufficiently small migration rate. For the proof we couple two processes and show that the density of the discrepancies goes to zero.

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Authors and Affiliations

  1. Department of Mathematics, White Hall, Cornell University, 14853, Ithaca, NY, USA

    Claudia Neuhauser

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  1. Claudia Neuhauser
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Neuhauser, C. An ergodic theorem for Schlögl models with small migration. Probab. Th. Rel. Fields 85, 27–32 (1990). https://doi.org/10.1007/BF01377625

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  • Received: 12 December 1988

  • Revised: 08 November 1989

  • Issue Date: March 1990

  • DOI: https://doi.org/10.1007/BF01377625

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Keywords

  • Migration
  • State Space
  • Stochastic Process
  • Random Walk
  • Probability Theory
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