带标记顶点的加尔顿-沃森树的惩罚化

Pub Date : 2024-08-12 DOI:10.1007/s10959-024-01364-y

Abraham Romain, Boulal Sonia, Debs Pierre

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引用次数: 0

摘要

我们考虑了一棵加尔顿-沃森树，在这棵树上，每个节点都是独立标记的，其概率取决于节点的外度。利用惩罚方法，我们展示了新的马丁格尔，其中标记数达到了 \(n-1\)级。然后，我们通过吉尔萨诺夫（Girsanov）变换利用这些马氏定理定义了新的概率度量，并描述了这些新概率下随机树的分布。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Penalization of Galton–Watson Trees with Marked Vertices

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Penalization of Galton–Watson Trees with Marked Vertices

We consider a Galton–Watson tree where each node is marked independently of each other with a probability depending on its out-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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