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Renewal theorem for a class of stationary sequences
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  • Published: June 1986

Renewal theorem for a class of stationary sequences

  • S. P. Lalley1 

Probability Theory and Related Fields volume 72, pages 195–213 (1986)Cite this article

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  • 15 Citations

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Summary

A renewal theorem is obtained for stationary sequences of the form ξn=ξ(...,X n-1,X n,X n+1...), whereX n,\(n \in \mathbb{Z}\), are i.i.d. r.v.s. valued in a Polish space. This class of processes is sufficiently broad to encompass functionals of recurrent Markov chains, functionals of stationary Gaussian processes, and functionals of one-dimensional Gibbs states. The theorem is proved by a new coupling construction.

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Authors and Affiliations

  1. Department of Mathematical Statistics, Columbia University, 10027, New York, NY, USA

    S. P. Lalley

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  1. S. P. Lalley
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Research supported by the National Science Foundation

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Lalley, S.P. Renewal theorem for a class of stationary sequences. Probab. Th. Rel. Fields 72, 195–213 (1986). https://doi.org/10.1007/BF00699103

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  • Received: 11 January 1985

  • Revised: 25 November 1985

  • Issue Date: June 1986

  • DOI: https://doi.org/10.1007/BF00699103

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Keywords

  • Markov Chain
  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Gaussian Process
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