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Ergodic properties of Poisson processes with almost periodic intensity
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  • Published: March 1990

Ergodic properties of Poisson processes with almost periodic intensity

  • Tomasz Rolski1 

Probability Theory and Related Fields volume 84, pages 27–37 (1990)Cite this article

Summary

We discuss in this paper a non-homogeneous Poisson process Π∘A driven by an almost periodic intensity function. We give the stationary version Π∘A * and the Palm version Π∘A 0 corresponding to Π∘A *. Let (T i ,i∈ℕ) be the inter-point distance sequence in Π∘A and (T 0 i ,i∈ℕ) in Π∘A 0. We prove that forj→∞, the sequence (T i+j,i∈ℕ) converges in distribution to (T 0i ,i∈ℕ). If the intensity function is periodic then the convergence is in variation.

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Authors and Affiliations

  1. Mathematical Institute, Wrocław University, pl. Grundwaldzki 2/4, 50-384, Wrocław, Poland

    Tomasz Rolski

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  1. Tomasz Rolski
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Rolski, T. Ergodic properties of Poisson processes with almost periodic intensity. Probab. Th. Rel. Fields 84, 27–37 (1990). https://doi.org/10.1007/BF01288556

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  • Received: 23 December 1986

  • Revised: 18 August 1988

  • Issue Date: March 1990

  • DOI: https://doi.org/10.1007/BF01288556

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Keywords

  • Stochastic Process
  • Probability Theory
  • Poisson Process
  • Mathematical Biology
  • Stationary Version
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