Distributional properties of first jump times of CBI processes with jump sizes in given Borel sets
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866915654071746560 |
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| author | Barczy, Matyas Palau, Sandra Xue, Yao |
| author_facet | Barczy, Matyas Palau, Sandra Xue, Yao |
| contents | We derive an expression for the joint distribution function of the first jump times of a continuous state and continuous time branching process with immigration (CBI process) with jump sizes in given Borel sets having finite total Lévy measures, which is defined as the sum of the measures appearing in the branching and immigration mechanisms of the CBI process in question. Our result generalizes a corresponding result of He and Li (2016), who considered this problem in case of a single Borel set having finite total Lévy measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04935 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distributional properties of first jump times of CBI processes with jump sizes in given Borel sets Barczy, Matyas Palau, Sandra Xue, Yao Probability 60J80, 60G55 We derive an expression for the joint distribution function of the first jump times of a continuous state and continuous time branching process with immigration (CBI process) with jump sizes in given Borel sets having finite total Lévy measures, which is defined as the sum of the measures appearing in the branching and immigration mechanisms of the CBI process in question. Our result generalizes a corresponding result of He and Li (2016), who considered this problem in case of a single Borel set having finite total Lévy measure. |
| title | Distributional properties of first jump times of CBI processes with jump sizes in given Borel sets |
| topic | Probability 60J80, 60G55 |
| url | https://arxiv.org/abs/2512.04935 |