TREE-VALUED MARKOV-CHAINS DERIVED FROM GALTON-WATSON PROCESSES

Authors
ALDOUS D PITMAN J
Citation
D. Aldous et J. Pitman, TREE-VALUED MARKOV-CHAINS DERIVED FROM GALTON-WATSON PROCESSES, Annales de l'I.H.P. Probabilites et statistiques, 34(5), 1998, pp. 637-686
Citations number
50
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Annales de l'I.H.P. Probabilites et statistiques → ACNP
ISSN journal
02460203
Volume
34
Issue
5
Year of publication
1998
Pages
637 - 686
Database
ISI
SICI code
0246-0203(1998)34:5<637:TMDFGP>2.0.ZU;2-K
Abstract
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 analo gous 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 condi tioned to be infinite. Results simplify and are further developed in t he special case of Poisson offspring distribution. (C) Elsevier, Paris .