Scaling limits for INAR$(\infty)$ processes
Probability
2025-05-19 v1
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 \cite{Wang2} and for the INAR(1) process as in \cite{Yu}.
Keywords
Cite
@article{arxiv.2505.10776,
title = {Scaling limits for INAR$(\infty)$ processes},
author = {Nian Yao},
journal= {arXiv preprint arXiv:2505.10776},
year = {2025}
}