Linking Stochastic Self-Propagating Star Formation and Spatio-Temporal Point Processes

The stochastic self-propagating star-formation (SSPSF) model is an important theoretical framework for explaining how localised star-formation events trigger subsequent activity across galactic discs. While widely used to interpret spiral and irregular structures, its probabilistic rules have lacked a formal statistical foundation. In this work, we establish a connection between the SSPSF model and spatio-temporal point processes (STPP), which describe events in space and time through history-dependent intensities. We show that the SSPSF update law is equivalent to a separable spatio-temporal Hawkes process, and we derive a simple likelihood function that recovers SSPSF parameters from historical star-formation event data under simplifying assumptions. Beyond the statistical formulation, the framework provides a new approach to analysing the propagation of star formation in galaxies, enabling observational surveys of star-forming regions to be interpreted within the STPP framework. Furthermore, the approach naturally extends to continuous-time models, offering a more realistic representation of galactic dynamics.