Normal approximation of Functionals of Point Processes: Application to Hawkes Processes
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912416453885952 |
|---|---|
| author | Coutin, Laure Massat, Benjamin Réveillac, Anthony |
| author_facet | Coutin, Laure Massat, Benjamin Réveillac, Anthony |
| contents | In this paper, we derive an explicit upper bound for the Wasserstein distance between a functional of point processes and a Gaussian distribution. Using Stein's method in conjunction with Malliavin's calculus and the Poisson embedding representation, our result applies to a variety of point processes including discrete and continuous Hawkes processes. In particular, we establish an explicit convergence rate for stable continuous non-linear Hawkes processes and for discrete Hawkes processes. Finally, we obtain an upper bound in the context of nearly unstable Hawkes processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19806 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Normal approximation of Functionals of Point Processes: Application to Hawkes Processes Coutin, Laure Massat, Benjamin Réveillac, Anthony Probability In this paper, we derive an explicit upper bound for the Wasserstein distance between a functional of point processes and a Gaussian distribution. Using Stein's method in conjunction with Malliavin's calculus and the Poisson embedding representation, our result applies to a variety of point processes including discrete and continuous Hawkes processes. In particular, we establish an explicit convergence rate for stable continuous non-linear Hawkes processes and for discrete Hawkes processes. Finally, we obtain an upper bound in the context of nearly unstable Hawkes processes. |
| title | Normal approximation of Functionals of Point Processes: Application to Hawkes Processes |
| topic | Probability |
| url | https://arxiv.org/abs/2407.19806 |