Related papers: Some properties of stationary continuous state bra…
We consider a fragmentation of discrete trees where the internal vertices are deleted independently at a rate proportional to their degree. Informally, the associated cut-tree represents the genealogy of the nested connected components…
Consider a population evolving as a discrete-time supercritical multi-type Galton--Watson process. Suppose we run the process for $T$ generations, then sample $k$ individuals uniformly at generation $T$ and trace their genealogy backwards…
We consider a branching random walk initiated by a single particle at location 0 in which particles alternately reproduce according to the law of a Galton-Watson process and disperse according to the law of a driftless random walk on the…
In this article, we consider a branching random walk on the real-line where displacements coming from the same parent have jointly regularly varying tails. The genealogical structure is assumed to be a supercritical Galton-Watson tree,…
It is well-known that 0 is the absorbing state for a branching system. Each particle in the system lives a random long time and gives a random number of new particles at its death time. It stops when the system has no particle. This paper…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
We consider an extended birth-death-immigration process defined on a lattice formed by the integers of $d$ semiaxes joined at the origin. When the process reaches the origin, then it may jumps toward any semiaxis with the same rate. The…
We consider the extinction events of Galton-Watson processes with countably infinitely many types. In particular, we construct truncated and augmented Galton-Watson processes with finite but increasing sets of types. A pathwise approach is…
This paper is concerned with an extended Galton-Watson process so as to allow individuals to live and reproduce for more than one unit time. We assume that each individual can live $k$ seasons (time-units) with probability $h_k$, and…
We introduce a branching process in a sparse random environment as an intermediate model between a Galton--Watson process and a branching process in a random environment. In the critical case we investigate the survival probability and…
We are interested in the dynamic of a structured branching population where the trait of each individual moves according to a Markov process. The rate of division of each individual is a function of its trait and when a branching event…
Consider a general branching process, a.k.a. Crump-Mode-Jagers process, generated by a perturbed random walk $\eta_1$, $\xi_1+\eta_2$, $\xi_1+\xi_2+\eta_3,\ldots$. Here, $(\xi_1,\eta_1)$, $(\xi_2, \eta_2),\ldots$ are independent identically…
We introduce a population dynamics model, where individual genomes are represented by bit-strings. Selection is described by death probabilities which depend on these genomes, and new individuals continuously replace the ones that die,…
In a Markov chain population model subject to catastrophes, random immigration events (birth), promoting growth, are in balance with the effect of binomial catastrophes that cause recurrent mass removal (death). Using a generating function…
In this manuscript, we continue with the systematic study of the speed of extinction of continuous state branching processes in L\'evy environments under more general branching mechanisms. Here, we deal with the weakly subcritical regime…
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…
We study the ergodic property of a continuous-state branching process with immigration and competition. The exponential ergodicity in a weighted total variation distance is proved under natural assumptions. The main theorem applies to…
We consider a general class of branching processes in discrete time, where particles have types belonging to a Polish space and reproduce independently according to their type. If the process is critical and the mean distribution of types…
We are interested in the evolving genealogy of a birth and death process with trait structure and ecological interactions. Traits are hereditarily transmitted from a parent to its offspring unless a mutation occurs. The dynamics may depend…
A branching random walk in presence of an absorbing wall moving at a constant velocity $v$ undergoes a phase transition as the velocity $v$ of the wall varies. Below the critical velocity $v_c$, the population has a non-zero survival…