Modelling Spatio-Temporal Cluster Point Processes: A Comprehensive Study of Hawkes models and Their Applications
- Autores: Alba Bernabeu Atanasio
- Directores de la Tesis: Jorge Mateu Mahiques (dir. tes.)
- Lectura: En la Universitat Jaume I ( España ) en 2026
- Idioma: inglés
- Número de páginas: 267
- Tribunal Calificador de la Tesis: Emanuele Giorgi (presid.) , Pablo Juan Verdoy (secret.) , Adina Alexandra Iftimi (voc.)
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- Resumen
Point processes are essential tools for modelling random phenomena occurring in space, time, or both, allowing analysis of the structure and dependence of discrete events within a continuous domain. Among the different types of processes, cluster processes are those where events tend to occur in close proximity, forming high-density regions. Within this framework, this thesis focuses on spatio-temporal Hawkes processes, a class of self-exciting point processes governed by an intensity function conditional on past events, describing how the occurrence of an event increases the likelihood of additional events in its temporal and spatial proximity. The research provides a comprehensive view of Hawkes processes and, complementarily, log-Gaussian Cox processes, combining literature review, simulation, inference, method comparison, and applications. The results improve the understanding of these clustering patterns, offer practical guidance for their application, and lay the foundations for future advances in the modelling and analysis of spatio-temporal phenomena.
