The pair correlation function of spatial Hawkes processes. (English) Zbl 1117.60052

Møller, Jesper; Torrisi, Giovanni Luca

Stat. Probab. Lett. 77, No. 10, 995-1003 (2007).

Summary: 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.

MSC:

60G55	Point processes (e.g., Poisson, Cox, Hawkes processes)
62M30	Inference from spatial processes

Keywords:

Bartlett spectrum; Hawkes process; pair correlation function; spatial point processes; summary statistics; unpredictable marks

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