Interacting point processes
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911209892085760 |
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| author | Cinque, Fabrizio Orsingher, Enzo |
| author_facet | Cinque, Fabrizio Orsingher, Enzo |
| contents | We study two different types of vector point processes with interacting components, introducing a migration-type effect. The first case concerns two groups which modify their states with rate functions depending on time only. This yields a representation of the vector process in terms of independent non-homogeneous Skellam processes. In the general case, the decomposition involves independent Poisson processes. The second model is a birth-death-migration vector process. In the case of the linear death-migration we show that, for a fixed time instant, the vector is equal in distribution to the sum of two independent Multinomial random variables. As a byproduct we derive the distribution of a pure migration process. Finally, we study the described vector processes time-changed with the inverse of Bernstein subordinator, establishing a general result concerning the relatioship between fractional difference-differential equations and the probability mass function of a wider class of point processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12531 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interacting point processes Cinque, Fabrizio Orsingher, Enzo Probability 60G55, 60G22 We study two different types of vector point processes with interacting components, introducing a migration-type effect. The first case concerns two groups which modify their states with rate functions depending on time only. This yields a representation of the vector process in terms of independent non-homogeneous Skellam processes. In the general case, the decomposition involves independent Poisson processes. The second model is a birth-death-migration vector process. In the case of the linear death-migration we show that, for a fixed time instant, the vector is equal in distribution to the sum of two independent Multinomial random variables. As a byproduct we derive the distribution of a pure migration process. Finally, we study the described vector processes time-changed with the inverse of Bernstein subordinator, establishing a general result concerning the relatioship between fractional difference-differential equations and the probability mass function of a wider class of point processes. |
| title | Interacting point processes |
| topic | Probability 60G55, 60G22 |
| url | https://arxiv.org/abs/2510.12531 |