Tree-Valued Markov Chains Derived From Galton-Watson Processes. (1997)
| Venue: | Ann. Inst. Henri Poincar'e |
| Citations: | 35 - 9 self |
BibTeX
@ARTICLE{Aldous97tree-valuedmarkov,
author = {David Aldous and Jim Pitman},
title = {Tree-Valued Markov Chains Derived From Galton-Watson Processes.},
journal = {Ann. Inst. Henri Poincar'e},
year = {1997},
volume = {34}
}
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Abstract
Let G be a Galton-Watson tree, and for 0 u 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 u 1) and an analogous process (G u ; 0 u 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. Running head. Tree-valued Markov chains. Key words. Borel distribution, branching process, conditioning, GaltonWatson process, generalized Poisson distribution, h-transform, pruning, random tree, size-biasing, spinal decomposition, thinning. AMS Subject classifications 05C80, 60C05, 60J27, 60J80 Research supported in part by N.S.F. Grants DMS9404345 and 9622859 1 Contents 1 Introduction 2 1.1 Related topics : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 2 Background and technical set-up 5 2.1 Notation and terminology for trees : : : : : : : : : : : : : : :...
