A new family of Markov branching trees: the alpha-gamma model

被引：26

作者：

Chen, Bo ^{[1
]}

Ford, Daniel ^{[2
]}

Winkel, Matthias ^{[1
]}

机构：

[1] Univ Oxford, Dept Stat, Oxford OX1 3TG, England

[2] Google Inc, Mountain View, CA 94043 USA

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2009年 / 14卷

关键词：

Alpha-gamma tree; splitting rule; sampling consistency; self-similar fragmentation; dislocation measure; continuum random tree; R-tree; Markov branching model; SELF-SIMILAR FRAGMENTATIONS; CONTINUUM RANDOM TREE;

D O I：

10.1214/EJP.v14-616

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 introduce a simple tree growth process that gives rise to a new two-parameter family of discrete fragmentation trees that extends Ford's alpha model to multifurcating trees and includes the trees obtained by uniform sampling from Duquesne and Le Gall's stable continuum random tree. We call these new trees the alpha-gamma trees. In this paper, we obtain their splitting rules, dislocation measures both in ranked order and in sized-biased order, and we study their limiting behaviour.

引用

页码：400 / 430

页数：31

共 24 条

[1] THE CONTINUUM RANDOM TREE-III [J].