Asymptotic Analysis of Discrete-Time Hawkes Process
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917324327485440 |
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| author | Sarma, Utpal Jyoti Deba Selvamuthu, Dharmaraja |
| author_facet | Sarma, Utpal Jyoti Deba Selvamuthu, Dharmaraja |
| contents | In a discrete-time setting, we consider an arrival process $\left\{ξ_n \, \middle| \, n = 1, 2, \ldots \right\}$, which models the occurrence of events, and a corresponding point process $\left\{H_n \, \middle| \, n = 1, 2, \ldots \right\}$, known as the discrete-time Hawkes process. These two stochastic processes are related by $H_n = \sum_{i=1}^n ξ_i$, and exhibit a self-exciting property. In particular, we study the limiting behavior of the arrival process and establish the Large Deviation Principle for the discrete-time Hawkes process. We also illustrate an application in which insurance claims are modeled using the discrete-time Hawkes process and analyze its behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08042 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic Analysis of Discrete-Time Hawkes Process Sarma, Utpal Jyoti Deba Selvamuthu, Dharmaraja Probability 60G55, 60F10, 60F05 In a discrete-time setting, we consider an arrival process $\left\{ξ_n \, \middle| \, n = 1, 2, \ldots \right\}$, which models the occurrence of events, and a corresponding point process $\left\{H_n \, \middle| \, n = 1, 2, \ldots \right\}$, known as the discrete-time Hawkes process. These two stochastic processes are related by $H_n = \sum_{i=1}^n ξ_i$, and exhibit a self-exciting property. In particular, we study the limiting behavior of the arrival process and establish the Large Deviation Principle for the discrete-time Hawkes process. We also illustrate an application in which insurance claims are modeled using the discrete-time Hawkes process and analyze its behavior. |
| title | Asymptotic Analysis of Discrete-Time Hawkes Process |
| topic | Probability 60G55, 60F10, 60F05 |
| url | https://arxiv.org/abs/2603.08042 |