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Equivalence of functional limit theorems for stationary point processes and their Palm distributions
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  • Published: May 1989

Equivalence of functional limit theorems for stationary point processes and their Palm distributions

  • Gert Nieuwenhuis1 nAff2 

Probability Theory and Related Fields volume 81, pages 593–608 (1989)Cite this article

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Summary

Let P be the distribution of a stationary point process on the real line and let P 0 be its Palm distribution. In this paper we consider two types of functional limit theorems, those in terms of the number of points of the point process in (0, t] and those in terms of the location of the nth point right of the origin. The former are most easily obtained under P and the latter under P 0. General conditions are presented that guarantee equivalence of either type of functional limit theorem under both probability measures, and under a third, P 1, which plays a role in the proofs and is obtained from P by shifting the origin to the first point of the process on the right.

In a brief final section the obtained results for either type of functional limit theorem are extended to equivalences between the two types by applying well-known results about processes drifting to infinity and the corresponding inverse processes.

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Author notes
  1. Gert Nieuwenhuis

    Present address: vakgroep Econometrie, Katholieke Universiteit Brabant, Hogeschoollaan 225, P.O. Box 90153, NL-5000 LE, Tilburg, The Netherlands

Authors and Affiliations

  1. Mathematisch Instituut, Katholieke Universiteit, Toernooiveld 5, NL-6525 ED, Nijmegen, The Netherlands

    Gert Nieuwenhuis

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  1. Gert Nieuwenhuis
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Nieuwenhuis, G. Equivalence of functional limit theorems for stationary point processes and their Palm distributions. Probab. Th. Rel. Fields 81, 593–608 (1989). https://doi.org/10.1007/BF00367306

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  • Issue Date: May 1989

  • DOI: https://doi.org/10.1007/BF00367306

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Keywords

  • Stochastic Process
  • General Condition
  • Probability Measure
  • Probability Theory
  • Stationary Point
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