Penalization of Galton–Watson Trees with Marked Vertices

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Theoretical Probability Pub Date : 2024-08-12 DOI:10.1007/s10959-024-01364-y

Abraham Romain, Boulal Sonia, Debs Pierre

引用次数: 0

Abstract

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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带标记顶点的加尔顿-沃森树的惩罚化

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。

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来源期刊

Journal of Theoretical Probability 数学-统计学与概率论

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Theoretical Probability publishes high-quality, original papers in all areas of probability theory, including probability on semigroups, groups, vector spaces, other abstract structures, and random matrices. This multidisciplinary quarterly provides mathematicians and researchers in physics, engineering, statistics, financial mathematics, and computer science with a peer-reviewed forum for the exchange of vital ideas in the field of theoretical probability.