  Many modern spatio-temporal data sets, in sociology, epidemiology or
seismology, for example, exhibit self-exciting characteristics, triggering and
clustering behaviors both at the same time, that a suitable Hawkes space-time
process can accurately capture. This paper aims to develop a fast and flexible
parametric inference technique to recover the parameters of the kernel
functions involved in the intensity function of a space-time Hawkes process
based on such data. Our statistical approach combines three key ingredients: 1)
kernels with finite support are considered, 2) the space-time domain is
appropriately discretized, and 3) (approximate) precomputations are used. The
inference technique we propose then consists of a $\ell_2$ gradient-based
solver that is fast and statistically accurate. In addition to describing the
algorithmic aspects, numerical experiments have been carried out on synthetic
and real spatio-temporal data, providing solid empirical evidence of the
relevance of the proposed methodology.
