Explosion rates for continuous-state branching processes in a Lévy environment
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913393784389632 |
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| author | Cardona-Tobón, Natalia Pardo, Juan Carlos |
| author_facet | Cardona-Tobón, Natalia Pardo, Juan Carlos |
| contents | Here, we study the long-term behaviour of the non-explosion probability for continuous-state branching processes in a Lévy environment when the branching mechanism is given by the negative of the Laplace exponent of a subordinator. In order to do so, we study the law of this family of processes in the infinite mean case and provide necessary and sufficient conditions for the process to be conservative, i.e. that the process does not explode in finite time a.s. In addition, we establish precise rates for the non-explosion probabilities in the subcritical and critical regimes, first found by Palau et al. [19] in the case when the branching mechanism is given by the negative of the Laplace exponent of a stable subordinator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03265 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Explosion rates for continuous-state branching processes in a Lévy environment Cardona-Tobón, Natalia Pardo, Juan Carlos Probability 60J80, 60G51, 60H10, 60K37 Here, we study the long-term behaviour of the non-explosion probability for continuous-state branching processes in a Lévy environment when the branching mechanism is given by the negative of the Laplace exponent of a subordinator. In order to do so, we study the law of this family of processes in the infinite mean case and provide necessary and sufficient conditions for the process to be conservative, i.e. that the process does not explode in finite time a.s. In addition, we establish precise rates for the non-explosion probabilities in the subcritical and critical regimes, first found by Palau et al. [19] in the case when the branching mechanism is given by the negative of the Laplace exponent of a stable subordinator. |
| title | Explosion rates for continuous-state branching processes in a Lévy environment |
| topic | Probability 60J80, 60G51, 60H10, 60K37 |
| url | https://arxiv.org/abs/2311.03265 |