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arXiv · 2403.00384

Penalization of Galton Watson trees with marked vertices

Romain Abraham·Sonia Boulal·Pierre Debs
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Abstract

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.

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Romain Abraham, Sonia Boulal, Pierre Debs. 2024-03-01. Penalization of Galton Watson trees with marked vertices. https://arxiv.org/abs/2403.00384

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