Scaling limits for INAR(∞) processes

2025/05/16 by Yao, Nian
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2505.10776

Abstract

In this paper, we study law of large numbers, central limit theorem, large and moderate deviations for INAR(∞) processes, which as a special case, includes both discrete-time linear Hawkes process and INAR(1) process in the literature. Our results recover existing results on large and moderate deviations for the discrete-time Hawkes process as studied in \citeWang2 and for the INAR(1) process as in \citeYu.

Citations

• Large and moderate deviations for a discrete-time marked Hawkes process
• Hawkes and INAR( ∞ ) processes
• Asymptotic behavior of unstable INAR( p ) processes
• Large deviations of Poisson cluster processes
• First-order observation-driven integer-valued autoregressive processes

Related

• Scaling limit of heavy tailed nearly unstable cumulative INAR(∞) processes and rough fractional diffusions
• Scaling limits for supercritical nearly unstable Hawkes processes
• Large deviations for the mean-field limit of Hawkes processes
• Precise Deviations for discrete marked Hawkes process
• Scaling limits for Hawkes processes and application to financial\n statistics