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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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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DOI: https://doi.org/10.1007/BF01288556
Keywords
- Stochastic Process
- Probability Theory
- Poisson Process
- Mathematical Biology
- Stationary Version