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On the correlation structure of some random point processes on the line

Author

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  • de Coninck, Joël
  • Dunlop, François
  • Huillet, Thierry

Abstract

The correlation structure of some remarkable point processes on the one-dimensional real line is investigated. More specifically, focus is on translation invariant determinantal, permanental and/or renewal point processes. In some cases, anomalous (non-Poissonian) fluctuations for the number of points in a large window can be observed. This may be read from the total correlation function of the point process. We try to understand when and why this occurs and what are the anomalous behaviors to be expected.

Suggested Citation

  • de Coninck, Joël & Dunlop, François & Huillet, Thierry, 2008. "On the correlation structure of some random point processes on the line," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(4), pages 725-744.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:4:p:725-744
    DOI: 10.1016/j.physa.2007.10.018
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    References listed on IDEAS

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    1. Daley, D.J. & Vesilo, Rein, 1997. "Long range dependence of point processes, with queueing examples," Stochastic Processes and their Applications, Elsevier, vol. 70(2), pages 265-282, October.
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    Cited by:

    1. Li, Ming, 2017. "Record length requirement of long-range dependent teletraffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 472(C), pages 164-187.
    2. Li, Ming & Li, Jia-Yue, 2017. "Generalized Cauchy model of sea level fluctuations with long-range dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 309-335.
    3. Li, Ming, 2020. "Multi-fractional generalized Cauchy process and its application to teletraffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).

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