A General Marked Point Process Framework For Self-Exciting Network Evolution

We propose a novel modeling framework for time-evolving networks allowing for long-term dependence in network features that update in continuous time. Dynamic network growth is functionally parameterized via the conditional intensity of a marked point process. This characterization enables flexible, joint modeling of both update timing and the network updates themselves, dependent on the entire left-continuous sample path. We propose a path dependent nonlinear marked Hawkes process as an expressive platform for modeling such data; its dynamic mark space embeds the time-evolving network. We prove well-posedness and establish sufficient stability conditions, demonstrate simulation and subsequent feasible likelihood-based inference through numerical study, and illustrate the methodology with an application to conference attendee social network data. The proposed formulation provides a flexible and principled foundation for statistical inference on complex network evolution in continuous time.