Penalization of Galton Watson trees with marked vertices
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914698205593600 |
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| author | Abraham, Romain Boulal, Sonia Debs, Pierre |
| author_facet | Abraham, Romain Boulal, Sonia Debs, Pierre |
| contents | We consider a Galton-Watson tree where each node is marked independently of each others with a probability depending on itsout-degree. Using a penalization method, we exhibit new martingales where the number of marks up to level n -- 1 appears. Then, we use these martingales to define new probability measures via a Girsanov transformation and describe the distribution of the random trees under these new probabilities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00384 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Penalization of Galton Watson trees with marked vertices Abraham, Romain Boulal, Sonia Debs, Pierre Probability We consider a Galton-Watson tree where each node is marked independently of each others with a probability depending on itsout-degree. Using a penalization method, we exhibit new martingales where the number of marks up to level n -- 1 appears. Then, we use these martingales to define new probability measures via a Girsanov transformation and describe the distribution of the random trees under these new probabilities. |
| title | Penalization of Galton Watson trees with marked vertices |
| topic | Probability |
| url | https://arxiv.org/abs/2403.00384 |