English

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(\infty) 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}
}
R2 v1 2026-06-28T23:35:12.926Z