A cluster representation of the renewal Hawkes process
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915362591735808 |
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| author | Ruíz, Luis Iván Hernández Yano, Kouji |
| author_facet | Ruíz, Luis Iván Hernández Yano, Kouji |
| contents | A cluster representation for a Hawkes process with renewal immigration is obtained. The centre and satellite processes are indicated as a renewal process and generalized branching processes respectively. It is confirmed that the proposed construction indeed represents a cluster process and it is verified that it admits the desired intensity. Finally, the probability generating functional is computed for the stationary limit case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_06288 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A cluster representation of the renewal Hawkes process Ruíz, Luis Iván Hernández Yano, Kouji Probability A cluster representation for a Hawkes process with renewal immigration is obtained. The centre and satellite processes are indicated as a renewal process and generalized branching processes respectively. It is confirmed that the proposed construction indeed represents a cluster process and it is verified that it admits the desired intensity. Finally, the probability generating functional is computed for the stationary limit case. |
| title | A cluster representation of the renewal Hawkes process |
| topic | Probability |
| url | https://arxiv.org/abs/2304.06288 |