Precise Deviations for discrete marked Hawkes processes

TL;DR

This paper investigates precise deviation probabilities for discrete marked Hawkes processes over large time scales, employing mod-$$ convergence theory to derive detailed asymptotic results.

Contribution

It introduces a novel application of mod-$$ convergence to analyze large and moderate deviations in discrete marked Hawkes processes.

Findings

Derived precise large deviation asymptotics

Established moderate deviation principles

Applied mod-$$ convergence to point process analysis

Abstract

In this paper, we study precise deviations including precise large deviations and moderate deviations for discrete marked Hawkes processes for large time asymptotics by using mod-$\phi$ convergence theory.