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Spatio-Temporal Hawkes Point Processes: A Review

Author

Listed:
  • Alba Bernabeu

    (University Jaume I)

  • Jiancang Zhuang

    (Research Organisation of Information and Systems
    The Graduate University for Advanced Studies
    London Mathematical Laboratory)

  • Jorge Mateu

    (University Jaume I)

Abstract

Hawkes processes are a particularly interesting class of stochastic point processes that were introduced in the early seventies by Alan Hawkes, notably to model the occurrence of seismic events. They are also called self-exciting point processes, in which the occurrence of an event increases the probability of occurrence of another event. The Hawkes process is characterized by a stochastic intensity, which represents the conditional probability density of the occurrence of an event in the immediate future, given the observations in the past. In this paper, we present some background and all major aspects of Hawkes processes, with a particular focus on simulation methods, and estimation techniques widely used in practical modeling aspects. We aim to provide a rich and self-contained overview of these stochastic processes as a way to have an overall vision of Hawkes processes in only one piece of paper. We also discuss possibilities for future research in the area of self-exciting processes.

Suggested Citation

  • Alba Bernabeu & Jiancang Zhuang & Jorge Mateu, 2025. "Spatio-Temporal Hawkes Point Processes: A Review," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 30(1), pages 89-119, March.
    • Handle: RePEc:spr:jagbes:v:30:y:2025:i:1:d:10.1007_s13253-024-00653-7
    DOI: 10.1007/s13253-024-00653-7
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