Continuum random trees and branching processes with immigration

DOI10.1016/j.spa.2006.04.016zbMath1161.60028arXivmath/0509519OpenAlexW2071988122MaRDI QIDQ1001842

Thomas S. A. Duquesne

Publication date: 19 February 2009

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0509519

zbMATH Keywords

invariance principleimmigrationlimit theoremRay-Knight theoremcontinuum random treeheight processLévy treecontinuous-state branching processGalton-Watson branching processcontour processsize-biased tree

Mathematics Subject Classification ID

Sample path properties (60G17) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Functional limit theorems; invariance principles (60F17)

Related Items (10)

Local convergence of critical random trees and continuous-state branching processes ⋮ A Lamperti-type representation of continuous-state branching processes with immigration ⋮ The Gorin-Shkolnikov identity and its random tree generalization ⋮ Lévy processes conditioned on having a large height process ⋮ Infinite stable looptrees ⋮ Scaling limit of linearly edge-reinforced random walks on critical Galton-Watson trees ⋮ Parabolic Anderson model on critical Galton-Watson trees in a Pareto environment ⋮ Fragmentation processes with an initial mass converging to infinity ⋮ Pruning of CRT-sub-trees ⋮ Exact simulation of the genealogical tree for a stationary branching population and application to the asymptotics of its total length

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