Some limit theorems for locally stationary Hawkes processes
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912208459399168 |
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| author | Deschatre, Thomas Gruet, Pierre Lotz, Antoine |
| author_facet | Deschatre, Thomas Gruet, Pierre Lotz, Antoine |
| contents | We prove a law of large numbers and functional central limit theorem for a class of multivariate Hawkes processes with time-dependent reproduction rate. We address the difficulties induced by the use of non-convolutive Volterra processes by recombining classical martingale methods introduced in Bacry et al. [3] with novel ideas proposed by Kwan et al. [19]. The asymptotic theory we obtain yields useful applications in financial statistics. As an illustration, we derive closed-form expressions for price distortions under liquidity constraints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17245 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some limit theorems for locally stationary Hawkes processes Deschatre, Thomas Gruet, Pierre Lotz, Antoine Probability 60F05, 60G55, 62M10, 62P05 We prove a law of large numbers and functional central limit theorem for a class of multivariate Hawkes processes with time-dependent reproduction rate. We address the difficulties induced by the use of non-convolutive Volterra processes by recombining classical martingale methods introduced in Bacry et al. [3] with novel ideas proposed by Kwan et al. [19]. The asymptotic theory we obtain yields useful applications in financial statistics. As an illustration, we derive closed-form expressions for price distortions under liquidity constraints. |
| title | Some limit theorems for locally stationary Hawkes processes |
| topic | Probability 60F05, 60G55, 62M10, 62P05 |
| url | https://arxiv.org/abs/2501.17245 |