Tail Asymptotics of Cluster Sizes in Multivariate Heavy-Tailed Hawkes Processes
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909563591065600 |
|---|---|
| author | Blanchet, Jose Laeven, Roger J. A. Wang, Xingyu Zwart, Bert |
| author_facet | Blanchet, Jose Laeven, Roger J. A. Wang, Xingyu Zwart, Bert |
| contents | We examine a distributional fixed-point equation related to a multi-type branching process that is key in the cluster sizes analysis of multivariate heavy-tailed Hawkes processes. Specifically, we explore the tail behavior of its solution and demonstrate the emergence of a form of multivariate hidden regular variation. Large values of the cluster size vector result from one or several significant jumps. A discrete optimization problem involving any given rare event set of interest determines the exact configuration of these large jumps and the degree of hidden regular variation. Our proofs rely on a detailed probabilistic analysis of the spatiotemporal structure of multiple large jumps in multi-type branching processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01004 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tail Asymptotics of Cluster Sizes in Multivariate Heavy-Tailed Hawkes Processes Blanchet, Jose Laeven, Roger J. A. Wang, Xingyu Zwart, Bert Probability We examine a distributional fixed-point equation related to a multi-type branching process that is key in the cluster sizes analysis of multivariate heavy-tailed Hawkes processes. Specifically, we explore the tail behavior of its solution and demonstrate the emergence of a form of multivariate hidden regular variation. Large values of the cluster size vector result from one or several significant jumps. A discrete optimization problem involving any given rare event set of interest determines the exact configuration of these large jumps and the degree of hidden regular variation. Our proofs rely on a detailed probabilistic analysis of the spatiotemporal structure of multiple large jumps in multi-type branching processes. |
| title | Tail Asymptotics of Cluster Sizes in Multivariate Heavy-Tailed Hawkes Processes |
| topic | Probability |
| url | https://arxiv.org/abs/2503.01004 |