Related papers: Long time behavior and Yaglom limit for real trait…
We consider birth-and-death processes of objects (animals) defined in ${\bf Z}^d$ having unit death rates and random birth rates. For animals with uniformly bounded diameter we establish conditions on the rate distribution under which the…
In the present paper, we characterize the behavior of supercritical branching processes in random environment with linear fractional offspring distributions, conditioned on having small, but positive values at some large generation. As it…
Let $Z_{n}$ be the number of individuals in a subcritical BPRE evolving in the environment generated by iid probability distributions. Let $X$ be the logarithm of the expected offspring size per individual given the environment. Assuming…
Multi-type birth-death processes underlie approaches for inferring evolutionary dynamics from phylogenetic trees across biological scales, ranging from deep-time species macroevolution to rapid viral evolution and somatic cellular…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
This paper deals into the long-term behavior of subordinated critical branching processes with migration. We focus on scenarios where emigration is the dominant factor and introduce additional randomness in timing through a subordination…
We study the asymptotics of the survival probability for the critical and decomposable branching processes in random environment and prove Yaglom type limit theorems for these processes. It is shown that such processes possess some…
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, we firstly determine the behavior of the successive hitting…
We investigate parameter estimation in subcritical continuous-time birth-and-death processes with multiple births. We show that the classical maximum likelihood estimators for the model parameters, based on the continuous observation of a…
We consider an indecomposable Galton-Watson branching process with countably infinitely many types. Assuming that the process is critical and allowing for infinite variance of the offspring sizes of some (or all) types of particles we…
We consider the classical Yaglom limit theorem for a branching Markov process $X = (X_t, t \ge 0)$, with non-local branching mechanism in the setting that the mean semigroup is critical, i.e. its leading eigenvalue is zero. In particular,…
A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $\lambda_n$ and a particle…
We study the existence and the exponential ergodicity of a general interacting particle system, whose components are driven by independent diffusion processes with values in an open subset of $\mathds{R}^d$, $d\geq 1$. The interaction…
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 populations which are initially large. Under general…
Many spatio-temporal data record the time of birth and death of individuals, along with their spatial trajectories during their lifetime, whether through continuous-time observations or discrete-time observations. Natural applications…
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…
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 study the first-passage properties of a jump process with constant drift where jump amplitudes and inter-arrival times follow arbitrary light-tailed distributions with smooth densities. Using a mapping to an effective discrete-time…
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…
Our principal aim is to observe the Markov discrete-time process of population growth with long-living trajectory. First we study asymptotical decay of generating function of Galton-Watson process for all cases as the Basic Lemma.…