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The pair correlation function of spatial Hawkes processes

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  • Møller, Jesper
  • Torrisi, Giovanni Luca

Abstract

Spatial Hawkes processes can be considered as spatial versions of classical Hawkes processes. We derive the pair correlation function of stationary spatial Hawkes processes and discuss the connection to the Bartlett spectrum and other summary statistics. Particularly, results for Gaussian fertility rates and the extension to spatial Hawkes processes with random fertility rates are discussed.

Suggested Citation

  • Møller, Jesper & Torrisi, Giovanni Luca, 2007. "The pair correlation function of spatial Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 995-1003, June.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:10:p:995-1003
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    References listed on IDEAS

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    1. Mugglestone, Moira A. & Renshaw, Eric, 1996. "A practical guide to the spectral analysis of spatial point processes," Computational Statistics & Data Analysis, Elsevier, vol. 21(1), pages 43-65, January.
    2. Yosihiko Ogata, 1998. "Space-Time Point-Process Models for Earthquake Occurrences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 379-402, June.
    3. Anders Brix & Jesper Moller, 2001. "Space‐time Multi Type Log Gaussian Cox Processes with a View to Modelling Weeds," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 471-488, September.
    4. Jesper Møller & Rasmus P. Waagepetersen, 2007. "Modern Statistics for Spatial Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 643-684, December.
    5. Jesper Møller & Jakob G. Rasmussen, 2006. "Approximate Simulation of Hawkes Processes," Methodology and Computing in Applied Probability, Springer, vol. 8(1), pages 53-64, March.
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    Cited by:

    1. Roueff, Francois & von Sachs, Rainer & Sansonnet, Laure, 2015. "Time-frequency analysis of locally stationary Hawkes processes," LIDAM Discussion Papers ISBA 2015011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Roueff, François & von Sachs, Rainer & Sansonnet, Laure, 2016. "Locally stationary Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 126(6), pages 1710-1743.

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