Tree-valued Markov chains derived from Galton-Watson processes

被引：71

作者：

Aldous, D ^{[1
]}

Pitman, J ^{[1
]}

机构：

[1] Univ Calif Berkeley, Dept Stat, Berkeley, CA 94720 USA

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 1998年 / 34卷 / 05期

关键词：

Borel distribution; branching process; conditioning; Galton-Watson process; generalized Poisson distribution; h-transform; pruning; random tree; size-biasing; spinal decomposition; thinning;

D O I：

10.1016/S0246-0203(98)80003-4

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：

Let G be a Galton-Watson tree, and for 0 less than or equal to u less than or equal to 1 let G(u) be the subtree of G obtained by retaining each edge with probability u. We study the tree-valued Markov process (G(u), 0 less than or equal to u less than or equal to 1) and an analogous process (G(u)*, 0 less than or equal to u less than or equal to 1) in which G(1)* is a critical or subcritical Galton-Watson tree conditioned to be infinite. Results simplify and are further developed in the special case of Poisson offspring distribution. (C) Elsevier, Paris.

引用

页码：637 / 686

页数：50

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