Related papers: Critical Branching Regenerative Processes with Mig…
This paper studies the asymptotic behavior of processes with switching. More precisely, the stability under fast switching for diffusion processes and discrete state space Markovian processes is considered. The proofs are based on…
For supercritical multitype branching processes in continuous time, we investigate the evolution of types along those lineages that survive up to some time t. We establish almost-sure convergence theorems for both time and population…
Conditional sampling distributions (CSDs), sometimes referred to as copying models, underlie numerous practical tools in population genomic analyses. Though an important application that has received much attention is the inference of…
We consider the branching process in random environment $\{Z_n\}_{n\geq 0}$, which is a~population growth process where individuals reproduce independently of each other with the reproduction law randomly picked at each generation. We…
The notion of stability can be generalised to point processes by defining the scaling operation in a randomised way: scaling a configuration by $t$ corresponds to letting such a configuration evolve according to a Markov branching particle…
We construct a modified continuous-state branching process whose Malthusian parameter is replaced by another when passing below a certain level. The construction is obtained via a Lamperti-like transform applied to a refracted L\'evy…
The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…
In this paper we study the conditional limit theorems for critical continuous-state branching processes with branching mechanism $\psi(\lambda)=\lambda^{1+\alpha}L(1/\lambda)$ where $\alpha\in [0,1]$ and $L$ is slowly varying at $\infty$.…
The vast majority of strategies aimed at controlling contagion processes on networks considers the connectivity pattern of the system as either quenched or annealed. However, in the real world many networks are highly dynamical and evolve…
It is well known that the behaviour of a branching process is completely described by the generating function of the offspring law and its fixed points. Branching random walks are a natural generalization of branching processes: a branching…
Recently, neuronal avalanches have been observed to display oscillations, a phenomenon regarded as the co-existence of a scale-free behaviour (the avalanches close to criticality) and scale-dependent dynamics (the oscillations). Ordinary…
We consider random walks in dynamic random environments which arise naturally as spatial embeddings of ancestral lineages in spatial locally regulated population models. In particular, as the main result, we prove the quenched central limit…
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…
An individual-based model of stochastic branching is proposed and studied, in which point particles drift in $\bar{\mathds{R}}_{+}:=[0,+\infty)$ towards the origin (edge) with unit speed, where each of them splits into two particles that…
In this paper we study the genealogical structure of a Galton-Watson process with neutral mutations, where the initial population is large and mutation rate is small \cite{B2}. Namely, we extend in two directions the results obtained in…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
We study a recently introduced ladder model which undergoes a transition between an active and an infinitely degenerate absorbing phase. In some cases the critical behaviour of the model is the same as that of the branching annihilating…
We study asymptotic behaviour of stochastic approximation procedures with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function.…
Migration between different habitats is ubiquitous among biological populations. In this Letter, we study a simple quasispecies model for evolution in two different habitats, with different fitness landscapes, coupled through one-way…
We consider a population of particles with unit life length. Dying each particle produces offspring whose size depends on the random environment specifying the reproduction law of all particles of the given generation and on the number of…