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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2505.10776 |
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| _version_ | 1866910947395764224 |
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| author | Yao, Nian |
| author_facet | Yao, Nian |
| contents | 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}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10776 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scaling limits for INAR$(\infty)$ processes Yao, Nian Probability 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}. |
| title | Scaling limits for INAR$(\infty)$ processes |
| topic | Probability |
| url | https://arxiv.org/abs/2505.10776 |