4 citations · 8 across the 12 of their papers we have counts for
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Threatening excursions in large population quasi-stationary birth and death systems. On a question of Antonio Galves
Pierre Collet, Servet Martínez, 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…
Branching diffusion processes and spectral properties of Feynman-Kac semigroup
Pierre Collet, Sylvie Méléard, Jaime San MARTIN
In this article we study the long time behavior of linear functionals of branching diffusion processesas well as the time reversal of the spinal process by means of spectral proper…
Sharp approximation and hitting times for stochastic invasion processes
Vincent Bansaye, Xavier Erny, Sylvie Méléard
We are interested in the invasion phase for stochastic processes with interactions when a single mutant with positive fitness arrives in a resident population at equilibrium. By a…
Filling the gap between individual-based evolutionary models and Hamilton-Jacobi equations
Nicolas Champagnat, Sylvie Méléard, Sepideh Mirrahimi +1
We consider a stochastic model for the evolution of a discrete population structured by a trait with values on a finite grid of the torus, and with mutation and selection. Traits a…
Large population limit of the spectrum of killed birth-and-death processes
J. -R. Chazottes, P. Collet, S. Méléard
We consider a general class of birth-and-death processes with state space which describes the size of a population going eventually to extinction with probabil…
Time reversal of spinal processes for linear and non-linear branching processes near stationarity
Benoît Henry, Sylvie Méléard, Viet Chi Tran
We consider a stochastic individual-based population model with competition, trait-structure affecting reproduction and survival, and changing environment. The changes of traits ar…
On time scales and quasi-stationary distributions for multitype birth-and-death processes
J. -R. Chazottes, P. Collet, S. Méléard
We consider a class of birth-and-death processes describing a population made of sub-populations of different types which interact with one another. The state space is $\mathbb…