Large and moderate deviations for a discrete-time marked Hawkes process

Abstract

Hawkes process is a continuous-time stochastic model that captures temporal stochastic self-exciting phenomena. In particular, the linear Hawkes process has been well studied and widely used in practice because of its mathematical tractability. However, in some contexts, a Hawkes model is not directly applicable because data is recorded in a discrete-time scheme or an aggregated way. Thus, a discrete-time Hawkes model is appealing for applications. In this paper, we study large and moderate deviations for a discrete-time marked Hawkes process first proposed in Xu, Zhu, and Wang (2020).