The genealogy of continuous-state branching processes with immigration

By Amaury Lambert. 2002

54 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Mathematical Physics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/aafaf70f1366525acb8904c76175b46332b9cbaf

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In Management Science and Operations Research

In Mathematical Physics

In Molecular Biology

Citations in the corpus

THE CONTOUR OF SPLITTING TREES IS A LÉVY PROCESS (2007, background): “Our result yields a new interpretation of a now famous connection between L´evy processes and branching processes [20, 9, 14] that can be worded as follows: the genealogy of (continuous-state) Markov branching processes can be coded by a scalar Markov process (called genealogy-coding process in…”
Invariance principles for random walks conditioned to stay positive (2006, methodology): “Similarly to the standard case, the genealogy of Galton–Watson and Lévy trees with immigration can be coded respectively by random walks and Lévy processes conditioned to stay positive, see Theorem 7 in [25].”
Population Dynamics and Random Genealogies (2008, background): “Actually, a generalization of this theorem can be found in Ref.[78].”
Coalescence times for the branching process (2003, background): “These processes appear as scaling limits of discrete branching processes (see [4], [7], [13]) and their genealogical structure has been recently investigated, see [3], [12], [14].”
Quasi-Stationary Distributions and the Continuous-State Branching Process Conditioned to Be Never Extinct (2007, background): “In order to understand better how the immigration occurs (see also (25)), we study the diffusion case (ψ is a quadratic polynomial) and the stable case (ψ is a power function with power α ∈ (1, 2]).”
The branching process with logistic growth (2005, background): “alogy of the LB-process, distribution of coalescence times.... In the pure branching case the ﬁrst of these 6 A. LAMBERT questions has an obvious answer, the others have been studied in particular in [2, 6, 10, 24, 25, 26, 28, 31]. The outline of the paper is straightforward. Section 2 is concerned ”