Abstract
In this paper, 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 modeling of both the time of updates 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 establish stability conditions, demonstrate simulation and subsequent feasible likelihood-based inference through numerical study, and present an application to conference attendee social network data. The resulting methodology serves as a general framework that can be readily adapted to a wide range of network topologies and point process model specifications.