Displaying similar documents to “Continuous-time multitype branching processes conditioned on very late extinction”

Continuous-time multitype branching processes conditioned on very late extinction

Sophie Pénisson (2012)

ESAIM: Probability and Statistics

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Multitype branching processes and Feller diffusion processes are conditioned on very late extinction. The conditioned laws are expressed as Doob -transforms of the unconditioned laws, and an interpretation of the conditioned paths for the branching process is given, the immortal particle. We study different limits for the conditioned process (increasing delay of extinction, long-time behavior, scaling limit) and provide an exhaustive list of exchangeability results.

A branching-selection process related to censored Galton–Walton processes

Olivier Couronné, Lucas Gerin (2014)

Annales de l'I.H.P. Probabilités et statistiques

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We obtain the asymptotics for the speed of a particular case of a particle system with branching and selection introduced by Bérard and Gouéré [ (2010) 323–342]. The proof is based on a connection with a supercritical Galton–Watson process at a certain level.

Microscopic concavity and fluctuation bounds in a class of deposition processes

Márton Balázs, Júlia Komjáthy, Timo Seppäläinen (2012)

Annales de l'I.H.P. Probabilités et statistiques

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We prove fluctuation bounds for the particle current in totally asymmetric zero range processes in one dimension with nondecreasing, concave jump rates whose slope decays exponentially. Fluctuations in the characteristic directions have order of magnitude 1/3. This is in agreement with the expectation that these systems lie in the same KPZ universality class as the asymmetric simple exclusion process. The result is via a robust argument formulated for a broad class of deposition-type...

Strong law of large numbers for branching diffusions

János Engländer, Simon C. Harris, Andreas E. Kyprianou (2010)

Annales de l'I.H.P. Probabilités et statistiques

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Let be the branching particle diffusion corresponding to the operator +(2−) on ⊆ℝ (where ≥0 and ≢0). Let denote the generalized principal eigenvalue for the operator + on and assume that it is finite. When >0 and +− satisfies certain spectral theoretical conditions, we prove that the random measure {− } converges almost surely in the vague topology as tends to infinity. This result...

Vasculogenesis Models Revisited - Measurement of VEGF Diffusion in Matrigel

T. Miura, R. Tanaka (2009)

Mathematical Modelling of Natural Phenomena

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The circulatory system is one of the first to function during development. The earliest event in the system's development is , whereby vascular progeniter cells form clusters called blood islands, which later fuse to form capillary networks. There exists a very good system that mimics this process. When HUVECs (Human Umbilical Vein Endothelial Cells) are cultured on Matrigel, they spontaneously form a capillary network structure. Two theoretical models have been proposed to explain...

Fluctuation limit theorems for age-dependent critical binary branching systems

José Alfredo López-Mimbela, Antonio Murillo-Salas (2011)

ESAIM: Proceedings

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We consider an age-dependent branching particle system in ℝ, where the particles are subject to -stable migration (0 <  ≤ 2), critical binary branching, and general (non-arithmetic) lifetimes distribution. The population starts off from a Poisson random field in ℝ with Lebesgue intensity. We prove functional central limit theorems and strong laws of large numbers under two rescalings: high particle density, and a space-time...