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Ergodicity of Spitzer's renewal model

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  • Sidoravicius, Vladas
  • Vares, Maria Eulália

Abstract

Answering a question raised in Andjel and Vares (1992), we prove the ergodicity of the infinite-dimensional renewal process whose coordinates are indexed by d and whose failure rate at any given site is the average of the ages of its neighbors plus a positive constant c, for any d >= 1, c> 0. The main point is to prove the convergence of zero boundary Gibbs measures as the volume tends to d. This also yields uniqueness of Gibbs measures.

Suggested Citation

  • Sidoravicius, Vladas & Vares, Maria Eulália, 1995. "Ergodicity of Spitzer's renewal model," Stochastic Processes and their Applications, Elsevier, vol. 55(1), pages 119-130, January.
    • Handle: RePEc:eee:spapps:v:55:y:1995:i:1:p:119-130
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    References listed on IDEAS

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    1. Andjel, Enrique D. & Vares, Maria E., 1992. "Ergodicity of an infinite dimensional renewal process," Stochastic Processes and their Applications, Elsevier, vol. 42(2), pages 215-236, September.
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