62 citations · 261 across the 37 of their papers we have counts for
38 papers · 1 filter
Invasion dynamics with vanishing fitness for a quasi-critical birth-death process
Vincent Bansaye, Nadia Belmabrouk, Xavier Erny +1
We study the invasion dynamics of populations exhibiting positive density-dependent effects. We start with a single individual and consider a single-type birth and death process. T…
Growing random planar network with oriented branching and fusion
Vincent Bansaye, Gael Raoul, Milica Tomasevic
We consider a growing planar network where a tip grows at constant speed, branches at constant rate and inactivates when it meets a branch already created. We only consider here or…
Strong law of large numbers and L log L condition for supercritical branching processes
Vincent Bansaye, Tresnia Berah, Bertrand Cloez
We consider branching processes for structured populations: each individual is characterized by a type or trait which belongs to a general measurable state space. We focus on the s…
Estimation of the lifetime distribution from fluctuations in Bellman-Harris processes
Jules Olayé, Hala Bouzidi, Andrey Aristov +4
The growth of a population is often modeled as branching process where each individual at the end of its life is replaced by a certain number of offspring. An example of these bran…
Branching process and homogeneization for epidemics on spatial random graphs
Vincent Bansaye, Michele Salvi
Consider a graph where the sites are distributed in space according to a Poisson point process on . We study a population evolving on this network, with individuals ju…
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…
A growth-fragmentation-isolation process on random recursive trees and contact tracing
Vincent Bansaye, Chenlin Gu, Linglong Yuan
We consider a random process on recursive trees, with three types of events. Vertices give birth at a constant rate (growth), each edge may be removed independently (fragmentation…
Spine for interacting populations and sampling
Vincent Bansaye
We consider Markov jump processes describing structured populations with interactions via density dependance. We propose a Markov construction with a distinguished individual which…
Scaling limits of bisexual Galton-Watson processes
Vincent Bansaye, Maria-Emilia Caballero, Sylvie Méléard +1
Bisexual Galton-Watson processes are discrete Markov chains where reproduction events are due to mating of males and females. Owing to this interaction, the standard branching prop…
A phase transition for large values of bifurcating autoregressive models
Vincent Bansaye, S. Valère Bitseki Penda
We describe the asymptotic behavior of the number of individuals with a large value in a stable bifurcating autoregressive process. The study of the associated fi…
Extinction rate of continuous state branching processes in critical Lévy environments
Vincent Bansaye, Juan Carlos Pardo, Charline Smadi
We study the speed of extinction of continuous state branching processes in a Lévy environment, where the associated Lévy process oscillates. Assuming that the Lévy process satisfi…
Scaling limits of general population processes - Wright-Fisher and branching processes in random environment
Vincent Bansaye, Maria-Emilia Caballero, Sylvie Méléard
Our motivation comes from the large population approximation of individual based models in population dynamics and population genetics. We propose a general method to investigate s…
Diffusions from Infinity
Vincent Bansaye, Pierre Collet, Servet Martinez +2
In this paper we consider diffusions on the half line (0, ) such that the expectation of the arrival time at the origin is uniformly bounded in the initial point. This impl…
Approximation of stochastic processes by non-expansive flows and coming down from infinity
Vincent Bansaye
We approximate stochastic processes in finite dimension by dynamical systems. We provide trajectorial estimates which are uniform with respect to the initial condition for a well c…
Queuing for an infinite bus line and aging branching process
Vincent Bansaye, Alain Camanes
We study a queueing system with Poisson arrivals on a bus line indexed by integers. The buses move at constant speed to the right and the time of service per customer getting on th…
Some stochastic models for structured populations : scaling limits and long time behavior
Vincent Bansaye, Sylvie Méléard
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a…
Speed of coming down from infinity for birth and death processes
Vincent Bansaye, Sylvie Méléard, Mathieu Richard
We finely describe the speed of "coming down from infinity" for birth and death processes which eventually become extinct. Under general assumptions on the birth and death rates, w…
Tightness for processes with fixed points of discontinuities and applications in varying environment
Vincent Bansaye, Tom Kurtz, Florian Simatos
We establish a sufficient condition for the tightness of a sequence of stochastic processes. Our condition makes it possible to study processes with accumulations of fixed times of…
Random walk with heavy tail and negative drift conditioned by its minimum and final values
Vincent Bansaye, Vladimir Vatutin
We consider random walks with finite second moment which drifts to and have heavy tail. We focus on the events when the minimum and the final value of this walk belong to…
How do birth and death processes come down from infinity?
Vincent Bansaye, Sylvie Méléard, Mathieu Richard
We finely describe the "coming down from infinity" for birth and death processes which eventually become extinct. Our biological motivation is to study the decrease of regulated po…
Ancestral lineages and limit theorems for branching Markov chains
Vincent Bansaye
We consider a branching model in discrete time where each individual has a trait in some general state space. Both the reproduction law and the trait inherited by the offsprings ma…
On the survival of a class of subcritical branching processes in random environment
Vincent Bansaye, Vladimir Vatutin
Let be the number of individuals in a subcritical BPRE evolving in the environment generated by iid probability distributions. Let be the logarithm of the expected offs…
Weak law of large numbers for some Markov chains along non homogeneous genealogies
Vincent Bansaye, Chunmao Huang
We consider a population with non-overlapping generations, whose size goes to infinity. It is described by a discrete genealogy which may be time non-homogeneous and we pay special…
On the extinction of Continuous State Branching Processes with catastrophes
Vincent Bansaye, Juan Carlos Pardo Millan, Charline Smadi
We consider continuous state branching processes (CSBP) with additional multiplicative jumps modeling dramatic events in a random environment. These jumps are described by a Lévy p…