Related papers: On Time-Changed Linear Birth-Death Process with Im…
We consider a multidimensional inhomogeneous birth-death process (BDP) and obtain bounds on the rate of convergence for the corresponding one-dimensional processes.
We study a pure death process. At each discrete time every individual dies or not independently of each other with a constant probability. We give examples showing that in a certain limit extinction happens along a path where one and only…
The spatial structure of an evolving population affects which mutations become fixed. Some structures amplify selection, increasing the likelihood that beneficial mutations become fixed while deleterious mutations do not. Other structures…
We study a model of growing population that competes for resources. At each time step, all existing particles reproduce and the offspring randomly move to neighboring sites. Then at any site with more than one offspring, the particles are…
Understanding the statistical properties of a collection of individuals subject to random displacements and birth-and-death events is key to several applications in physics and life sciences, encompassing the diagnostic of nuclear reactors…
We develop a likelihood-based inference for finite-state birth-death processes with composite birth rates, in which multiple distinct mechanisms contribute additively to the total birth intensity. Our main motivating example is an SIS…
Motivated by modeling the dynamics of a population living in a flowing medium where the environmental factors are random in space, we have studied an asymmetric variant of the one-dimensional contact process, where the quenched random…
In this paper, we review recent results of ours concerning branching processes with general lifetimes and neutral mutations, under the infinitely many alleles model, where mutations can occur either at birth of individuals or at a constant…
A Galton-Watson branching process with immigration evolving in a random environment is considered. Its associated random walk is assumed to be oscillating. We prove a functional limit theorem in which the process under consideration is…
The binary branching Brownian motion in the boundary case is a particle system on the real line behaving as follows. It starts with a unique particle positioned at the origin at time $0$. The particle moves according to a Brownian motion…
We study simple stochastic scenarios, based on birth-and-death Markovian processes, that describe populations with Allee effect, to account for the role of demographic stochasticity. In the mean-field deterministic limit we recover…
Many scientific questions can be framed as asking for a first passage time (FPT), which generically describes the time it takes a random "searcher" to find a "target." The important timescale in a variety of biophysical systems is the time…
In this paper, we consider time-inhomogeneous branching processes and time-inhomogeneous birth-and-death processes, in which the offspring distribution and birth and death rates (respectively) vary in time. A classical result of branching…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
It is known that the time until a birth and death process reaches a certain level is distributed as a sum of independent exponential random variables. Diaconis, Miclo and Swart gave a probabilistic proof of this fact by coupling the birth…
The generalized Fleming-Viot processes were defined in 1999 by Donnelly and Kurtz using a particle model and by Bertoin and Le Gall in 2003 using stochastic flows of bridges. In both methods, the key argument used to characterize these…
We consider a class of birth-and-death processes describing a population made of $d$ sub-populations of different types which interact with one another. The state space is $\mathbb{Z}_+^d$ (unbounded). We assume that the population goes…
A birth-death-move process with mutations is a Markov model for a system of marked particles in interaction, that move over time, with births and deaths. In addition the mark of each particle may also change, which constitutes a mutation.…
By a random process with immigration at random times we mean a shot noise process with a random response function (response process) in which shots occur at arbitrary random times. The so defined random processes generalize random processes…
Understanding whether a population will survive and flourish or become extinct is a central question in population biology. One way of exploring this question is to study population dynamics using reaction-diffusion equations, where…