Related papers: Explosion and non-explosion in pure birth Crump--M…
The problem of conditioning a continuous-state branching process with quadratic competition (logistic CB process) on non-extinction is investigated. We first establish that non-extinction is equivalent to the total progeny of the population…
In this paper we prove the necessity of the main sufficient condition of Meinardus for sub exponential rate of growth of the number of structures, having multiplicative generating functions of a general form and establish a new necessary…
This work considers a chemotaxis system for multi-species that includes birth or death rate terms, which implies no mass preservation of the populations. We aim to show the convergence to a $L^{\infty}\ -\ $weak solutions, that is local in…
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…
It is well known that a simple, supercritical Bienaym\'e-Galton-Watson process turns into a subcritical such process, if conditioned to die out. We prove that the corresponding holds true for general, multi-type branching, where…
We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…
We introduce and study the class of branching-stable point measures, which can be seen as an analog of stable random variables when the branching mechanism for point measures replaces the usual addition. In contrast with the classical…
Let $\omega=(\omega_i)_{i\in\mathbb Z}=(\mu^{L}_i,...,\mu^{1}_i,\lambda_i)_{i\in \mathbb Z}$, which serves as the environment, be a sequence of i.i.d. random nonnegative vectors, with $L\ge1$ a positive integer. We study birth and death…
Stochastic modelling of fatigue (and other material's deterioration), as well as of cumulative damage in risk theory, are often based on compound sums of independent random variables, where the number of addends is represented by an…
Chen [Ann. Appl. Probab. {\bf 11} (2001), 1242--1262] derived exact convergence rates in a central limit theorem and a local limit theorem for a supercritical branching Wiener process.We extend Chen's results to a branching random walk…
This paper is concerned with Crump-Mode-Jagers branching processes, describing spread of an epidemic depending on the proportion of the population that is vaccinated. Births in the branching process are aborted independently with a…
Let $X_n(k)$ be the number of vertices at level $k$ in a random recursive tree with $n+1$ vertices. We prove a functional limit theorem for the vector-valued process $(X_{[n^t]}(1),\ldots, X_{[n^t]}(k))_{t\geq 0}$, for each $k\in\mathbb N$.…
Consider a supercritical Crump--Mode--Jagers process $(\mathcal Z_t^{\varphi})_{t \geq 0}$ counted with a random characteristic $\varphi$. Nerman's celebrated law of large numbers [Z. Wahrsch. Verw. Gebiete 57, 365--395, 1981] states that,…
The linear-fractional Galton-Watson processes is a well known case when many characteristics of a branching process can be computed explicitly. In this paper we extend the two-parameter linear-fractional family to a much richer…
Continuous-time branching processes describe the evolution of a population whose individuals generate a random number of children according to a birth process. Such branching processes can be used to understand preferential attachment…
Explosive events from magnetars are likely due to the catastrophic release of stress in their crusts, but the behavior of crustal matter beyond linear elasticity is poorly understood. We argue here that seminal results from molecular…
We establish general theorems quantifying the notion of recurrence --- through an estimation of the moments of passage times --- for irreducible continuous-time Markov chains on countably infinite state spaces. Sharp conditions of…
A proof is developed from first principles, independent of general relativity and of thermodynamics, that there exists a threshold acceleration above which radiation (real particle creation) from the vacuum must occur. The radiation is not…
The boundary behavior of continuous-state branching processes with quadratic competition is studied in whole generality. We first observe that despite competition, explosion can occur for certain branching mechanisms. We obtain a necessary…
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 focus…