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Point processes characterized by their one dimensional distributions
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  • Published: 26 November 2003

Point processes characterized by their one dimensional distributions

  • Aihua Xia1 

Probability Theory and Related Fields volume 128, pages 467–474 (2004)Cite this article

Abstract.

It is well-known that the distribution of a point process Ξ defined on a carrier space Γ is uniquely characterised by its finite dimensional joint distributions of counts on disjoint subsets of Γ. In this note, we investigate the common structure of point processes whose distributions are specified by their one dimensional distributions. We also show that, if Ξ is such a point process, then a sequence of point processes {Ξ n } converges in distribution to Ξ if and only if {Ξ n (B)} converges in distribution to Ξ(B) for a suitably rich class of sets B⊂Γ.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, The University of Melbourne, VIC 3010, Australia

    Aihua Xia

Authors
  1. Aihua Xia
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Corresponding author

Correspondence to Aihua Xia.

Additional information

Supported by ARC Discovery project number DP0209179

Mathmatics Subject Classification (2000): Primary 60G55; Secondary 60E05, 60B10

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Cite this article

Xia, A. Point processes characterized by their one dimensional distributions. Probab. Theory Relat. Fields 128, 467–474 (2004). https://doi.org/10.1007/s00440-003-0314-y

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  • Received: 22 June 2003

  • Revised: 12 September 2003

  • Published: 26 November 2003

  • Issue Date: March 2004

  • DOI: https://doi.org/10.1007/s00440-003-0314-y

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Keywords

  • Point process
  • Simple point process
  • Ordinary point process
  • Weakly ordinary point process
  • Poisson process
  • Finite dimensional distribution
  • Probability generating function
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