The exact packing measure of Levy trees

被引：5

作者：

Duquesne, Thomas ^{[1
]}

机构：

[1] Univ Paris 06, Lab Probabilites & Modeles Aleatoires, F-75252 Paris 05, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2012年 / 122卷 / 03期

关键词：

Branching processes; Levy trees; Mass measure; Packing measure; SELF-SIMILAR FRAGMENTATIONS; CONTINUUM RANDOM TREE; THEOREM; GROWTH;

D O I：

10.1016/j.spa.2011.10.013

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 study fine properties of Levy trees that are random compact metric spaces introduced by Le Gall and Le Jan in 1998 as the genealogy of continuous state branching processes. Levy trees are the scaling limits of Galton-Watson trees and they generalize the Aldous continuum random tree which corresponds to the Brownian case. In this paper, we prove that Levy trees always have an exact packing measure: we explicitly compute the packing gauge function and we prove that the corresponding packing measure coincides with the mass measure up to a multiplicative constant. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：968 / 1002

页数：35

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