Related papers: Non-binary branching process and Non-Markovian exp…
Branching processes are classical growth models in cell kinetics. In their construction, it is usually assumed that cell lifetimes are independent random variables, which has been proved false in experiments. Models of dependent lifetimes…
We consider subcritical branching processes with immigration which evolve under the influence of a random environment and study the tail distribution of life periods of such processes defined as the length of the time interval between the…
Let $\tau$n be a random tree distributed as a Galton-Watson tree with geometric offspring distribution conditioned on {Zn = an} where Zn is the size of the n-th generation and (an, n $\in$ N *) is a deterministic positive sequence. We study…
In this article, we focus on Bienaym\'e-Galton-Watson processes with linear-fractional offspring distributions. At a fixed generation, we consider a sample of the individuals alive, drawn in two different ways: either through Bernoulli…
We consider a super-critical Galton-Watson tree whose non-degenerate offspring distribution has finite mean. We consider the random trees $\tau$n distributed as $\tau$ conditioned on the n-th generation, Zn, to be of size an $\in$ N. We…
In this paper we consider inhomogeneous Galton-Watson trees, and derive various moments for such processes: the number of vertices, the number of leaves, and the height of the tree. Also we make a simple condition of finiteness. We use…
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…
In this paper, we study a parallel version of Galton-Watson processes for the random generation of tree-shaped structures. Random trees are useful in many situations (testing, binary search, simulation of physics phenomena,...) as attests…
We are interested in the genealogical structure of alleles for a Bienaym\'e-Galton-Watson branching process with neutral mutations (infinite alleles model), in the situation where the initial population is large and the mutation rate small.…
In this paper we consider a random walk in random environment on a tree and focus on the boundary case for the underlying branching potential. We study the range $R\_n$ of this walk up to time $n$ and obtain its correct asymptotic in…
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…
Understanding the evolution of binary traits, which affects the birth and survival of species and also the rate of molecular evolution, remains challenging. A typical example is the evolution of mating systems in plant species. In this…
We consider a branching-selection particle system on the real line. In this model the total size of the population at time $n$ is limited by $\exp\left(a n^{1/3}\right)$. At each step $n$, every individual dies while reproducing…
We consider population-size-dependent branching processes (PSDBPs) which eventually become extinct with probability one. For these processes, we derive maximum likelihood estimators for the mean number of offspring born to individuals when…
A decomposable strongly critical Galton-Watson branching process with $N$ types of particles labelled $1,2,...,N$ is considered in which a type~$i$ parent may produce individuals of types $j\geq i$ only. This model may be viewed as a…
A density-dependent branching process is a particle system in which individuals reproduce independently, but in a way that depends on the current population size. This feature can model a wide range of ecological interactions at the cost of…
Stem cells, through their ability to produce daughter stem cells and differentiate into specialized cells, are essential in the growth, maintenance, and repair of biological tissues. Understanding the dynamics of cell populations in the…
(Multi-type) branching processes are a natural and well-studied model for generating random infinite trees. Branching processes feature both nondeterministic and probabilistic branching, generalizing both transition systems and Markov…
We establish the joint scaling limit of a critical Bienaym\'e-Galton-Watson process with immigration (BGWI) and its (counting) local time at zero to the corresponding self-similar continuous-state branching process with immigration (CBI)…
We code Galton-Walton trees by a continuous height process, in order to give a precise meaning to the convergence of forests of trees. This allows us to establish the convergence of the forest of genealogical trees of the branching process…