Pruning Galton–Watson trees and tree-valued Markov processes
نویسندگان
چکیده
منابع مشابه
Pruning Galton-Watson Trees and Tree-valued Markov Processes
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 {G(u)} by pruning Galton-Watson trees and an analogous process {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 ...
متن کاملTree-valued Markov Chains Derived from Galton-watson Processes
Let G be a Galton-Watson tree, and for 0 u 1 let Gu be the subtree of G obtained by retaining each edge with probability u. We study the tree-valued Markov process (Gu; 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 in nite. Results simplify and are further developed in the special case of Poisson( ) o spring distribut...
متن کاملA Continuum - Tree - Valued Markov Process
We present a construction of a Lévy continuum random tree (CRT) associated with a super-critical continuous state branching process using the so-called exploration process and a Girsanov theorem. We also extend the pruning procedure to this super-critical case. Let ψ be a critical branching mechanism. We set ψθ(·) = ψ(·+ θ)− ψ(θ). Let Θ = (θ∞,+∞) or Θ = [θ∞,+∞) be the set of values of θ for whi...
متن کاملTree Structured Qbd Markov Chains and Tree-like Qbd Processes
In this paper we show that an arbitrary tree structured QBD Markov chain can be embedded in a tree-like QBD process with a special structure. Moreover, we present an algebraic proof that applying the natural fixed point iteration (FPI) to the nonlinear matrix equation V = B + ∑d s=1 Us(I − V )Ds that solves the tree-like QBD process, is equivalent to the more complicated iterative algorithm pre...
متن کاملTree-valued Markov chains and Poisson-Galton-Watson distributions
The Poisson-Galton-Watson distribution on nite trees, and the related PGW 1 (1) distribution on innnite trees with one end, arise in several contexts, in particular as n ! 1 weak limits within various size-n combinato-rial models. We review this topic, introducingslick notation for describing such distributions. We then describe a family of continuous-time Markov chains whose marginal distribut...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
سال: 2012
ISSN: 0246-0203
DOI: 10.1214/11-aihp423