4 papers · 1 filter
Threatening excursions in large population quasi-stationary birth and death systems. On a question of Antonio Galves
Pierre Collet, Servet MartÃnez, Sylvie Méléard
We consider time continuous multispecies birth and death processes in a regime of large populations. The jump rates depend on a large scaling parameter K modeling the charge capaci…
From stochastic individual-based models to free-boundary Hamilton-Jacobi equations
Nicolas Champagnat, Sylvie Méléard, Sepideh Mirrahimi +1
We study a stochastic branching model for a population structured by a quantitative phenotypic trait and subject to births, deaths, and mutations. In a regime of large population a…
Hematopoiesis as a continuum: from stochastic compartmental model to hydrodynamic limit
Vincent Bansaye, Ana Fernández Baranda, Stéphane Giraudier +1
We consider a multiscale stochastic compartmental model with three types of cells (stem cells, immature cells and mature cells) which combines cell proliferation and cell different…
Long time behavior and Yaglom limit for real trait-structured Birth and Death Processes
Pierre Collet, Sylvie Méléard, Jaime San
In this article we study the long time behaviour of measure-valued birth and death processes in continuous time, where the dynamics between jumps are one-dimensional Markov process…