Spinal constructions for continuous type-space branching processes with interactions
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911876299882496 |
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| author | Medous, Charles |
| author_facet | Medous, Charles |
| contents | We consider branching processes describing structured, interacting populations in continuous time. Dynamics of each individuals characteristics and branching properties can be influenced by the entire population. We propose a Girsanov-type result based on a spinal construction, and establish a many-to-one formula. By combining this result with the spinal decomposition, we derive a generalized continuous-time version of the Kesten-Stigum theorem that incorporates interactions. Additionally, we propose an alternative approach of the spine construction for exact simulations of stochastic size-dependent populations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_15449 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spinal constructions for continuous type-space branching processes with interactions Medous, Charles Probability 60J80, 60J85, 60H30 We consider branching processes describing structured, interacting populations in continuous time. Dynamics of each individuals characteristics and branching properties can be influenced by the entire population. We propose a Girsanov-type result based on a spinal construction, and establish a many-to-one formula. By combining this result with the spinal decomposition, we derive a generalized continuous-time version of the Kesten-Stigum theorem that incorporates interactions. Additionally, we propose an alternative approach of the spine construction for exact simulations of stochastic size-dependent populations. |
| title | Spinal constructions for continuous type-space branching processes with interactions |
| topic | Probability 60J80, 60J85, 60H30 |
| url | https://arxiv.org/abs/2309.15449 |