The stable trees are nested

被引：10

作者：

Curien, Nicolas ^{[1
]}

Haas, Benedicte ^{[1
,2
]}

机构：

[1] Ecole Normale Super, F-75231 Paris, France

[2] Univ Paris 09, Paris, France

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2013年 / 157卷 / 3-4期

关键词：

Stable Levy trees; Pruning; Dissipative self-similar fragmentations; Marchal's algorithm; SELF-SIMILAR FRAGMENTATIONS; BRANCHING-PROCESSES; GALTON-WATSON;

D O I：

10.1007/s00440-012-0472-x

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We show that we can construct simultaneously all the stable trees as a nested family. More precisely, if we prove that hidden inside any -stable tree we can find a version of an -stable tree rescaled by an independent Mittag-Leffler type distribution. This tree can be explicitly constructed by a pruning procedure of the underlying stable tree or by a modification of the fragmentation associated with it. Our proofs are based on a recursive construction due to Marchal which is proved to converge almost surely towards a stable tree.

引用

页码：847 / 883

页数：37

共 26 条

[1] Pruning a Levy continuum random tree [J].