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Pruning Galton-Watson Trees and Tree-valued Markov Processes
- Source :
- Annales de l'Institut Henri Poincar\'e (B) Probabilit\'es et Statistiques 48, 3 (2012) 688-705
- Publication Year :
- 2010
-
Abstract
- We present a new pruning procedure on discrete trees by adding marks on the nodes of trees. This procedure allows us to construct and study a tree-valued Markov process $\{{\cal G}(u)\}$ by pruning Galton-Watson trees and an analogous process $\{{\cal G}^*(u)\}$ by pruning a critical or subcritical Galton-Watson tree conditioned to be infinite. Under a mild condition on offspring distributions, we show that the process $\{{\cal G}(u)\}$ run until its ascension time has a representation in terms of $\{{\cal G}^*(u)\}$. A similar result was obtained by Aldous and Pitman (1998) in the special case of Poisson offspring distributions where they considered uniform pruning of Galton-Watson trees by adding marks on the edges of trees.
- Subjects :
- Mathematics - Probability
Subjects
Details
- Database :
- arXiv
- Journal :
- Annales de l'Institut Henri Poincar\'e (B) Probabilit\'es et Statistiques 48, 3 (2012) 688-705
- Publication Type :
- Report
- Accession number :
- edsarx.1007.0370
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1214/11-AIHP423