Critical multitype branching: a functional limit theorem and ancestral processes
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912355153084416 |
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| author | Baake, Ellen Cordero, Fernando Mellis, Sophia-Marie Wachtel, Vitali |
| author_facet | Baake, Ellen Cordero, Fernando Mellis, Sophia-Marie Wachtel, Vitali |
| contents | We consider the long-term behaviour of critical multitype branching processes conditioned on non-extinction, both with respect to the forward and the ancestral processes. Forward in time, we prove a functional limit theorem in the space of trajectories of the linearly-scaled $h$-transformed process; the change of measure allows us to work on the same probability space for all times. Backward in time, we trace the lines of descent of individuals sampled from a (stationary) population and analyse the ancestral type distribution, that is, the type distribution of the ancestors in the distant past, as well as the type process along the ancestral line. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21714 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Critical multitype branching: a functional limit theorem and ancestral processes Baake, Ellen Cordero, Fernando Mellis, Sophia-Marie Wachtel, Vitali Probability 60J80, 60F10 We consider the long-term behaviour of critical multitype branching processes conditioned on non-extinction, both with respect to the forward and the ancestral processes. Forward in time, we prove a functional limit theorem in the space of trajectories of the linearly-scaled $h$-transformed process; the change of measure allows us to work on the same probability space for all times. Backward in time, we trace the lines of descent of individuals sampled from a (stationary) population and analyse the ancestral type distribution, that is, the type distribution of the ancestors in the distant past, as well as the type process along the ancestral line. |
| title | Critical multitype branching: a functional limit theorem and ancestral processes |
| topic | Probability 60J80, 60F10 |
| url | https://arxiv.org/abs/2504.21714 |