WebJan 11, 2012 · We obtain a representation of Feller’s branching diffusion with logistic growth in terms of the local times of a reflected Brownian motion H with a drift that is affine linear in the local time accumulated by H at its current level. As in the classical Ray–Knight representation, the excursions of H are the exploration paths of the trees of descendants … WebBased on an intuitive approach to the Ray-Knight representation of Feller’s branching diffusion in terms of Brownian excursions we survey a few recent developments around exploration and mass excursions. One of these is Bertoin’s “tree of alleles with rare mutations” [6], seen as a tree of excursions of Feller’s branching diffusion. Another …

“Trees under attack”: a Ray–Knight representation of Feller’s branching …

WebBranching process with diffusion. A model of a branching process in which the reproducing particles diffuse in some domain $ G $. Let the domain $ G $ be $ r $- dimensional, with an absorbing boundary $ \partial G $, and let the particles in the domain itself execute mutually independent Brownian motions. Each particle in $ G $ is … Webalso referred to as the branching property. Consider now, instead of a Feller branching diffusion, the same SDE with a logistic drift, namely dZx t= h θZx t −γ(Ztx) 2 i dt+2 p Zx t dW , Z x 0 = x, (1) where θ,γ > 0 are given parameters which will be fixed throughout the paper, and x > 0 is the initial population. Just like Feller’s ... blue and white striped long skirt

From exploration paths to mass excursions - Semantic Scholar

Web2011 From Brownian motion with a local time drift to Feller's branching diffusion with logistic growth. Etienne Pardoux, Anton Wakolbinger. Author Affiliations + Electron. … WebApr 2, 2010 · Branching Feller diffusion for cell division with parasite infection. We describe the evolution of the quantity of parasites in a population of cells which divide in continuous-time. The quantity of parasites in a cell follows a Feller diffusion, which is splitted randomly between the two daughter cells when a division occurs. WebFor a coupling due to Dawson and Li, which in case of a linear drift describes the corresponding Feller branching diffusion, and in our case makes the path-valued … blue and white striped pants men