相关论文: On the uniqueness of quasi-stationary distribution…

We study a class of multi-species birth-and-death processes going almost surely to extinction and admitting a unique quasi-stationary distribution (qsd for short). When rescaled by $K$ and in the limit $K\to+\infty$, the realizations of…

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 study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric…

For a time-changed symmetric $\alpha$-stable process killed upon hitting zero, under the condition of entrance from infinity, we prove the existence and uniqueness of quasi-stationary distribution (QSD). The exponential convergence to the…

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…

The present paper is devoted to the investigation of the long term behavior of a class of singular multi-dimensional diffusion processes that get absorbed in finite time with probability one. Our focus is on the analysis of quasi-stationary…

In this paper, we study quasi-stationary distributions (QSDs) for one-dimensional diffusions killed at 0, when 0 is a regular boundary and $+\infty$ is a natural boundary. More precisely, we not only give a necessary and sufficient…

This article studies the quasi-stationary behaviour of population processes with unbounded absorption rate, including one-dimensional birth and death processes with catastrophes and multi-dimensional birth and death processes, modeling…

For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. Interestingly there is the possibility that the…

We characterise all the quasi-stationary distributions and the Q-process associated with a continuous state branching process that explodes in finite time. We also provide a rescaling for the continuous state branching process conditioned…

This survey concerns the study of quasi-stationary distributions with a specific focus on models derived from ecology and population dynamics. We are concerned with the long time behavior of different stochastic population size processes…

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…

This paper is a collection of recent results on discrete-time and continuous-time branching random walks. Some results are new and others are known. Many aspects of this theory are considered: local, global and strong local survival, the…

The stationary asymptotic properties of the diffusion limit of a multi-type branching process with neutral mutations are studied. For the critical and subcritical processes the interesting limits are those of quasi-stationary distributions…

In the setting of stochastic dynamical systems that eventually go extinct, the quasi-stationary distributions are useful to understand the long-term behavior of a system before evanescence. For a broad class of applicable continuous-time…

We consider the genealogical tree of a stationary continuous state branching process with immigration. For a sub-critical stable branching mechanism, we consider the genealogical tree of the extant population at some fixed time and prove…

We consider an irreducible pure jump Markov process with rates Q=(q(x,y)) on \Lambda\cup\{0\} with \Lambda countable and 0 an absorbing state. A quasi-stationary distribution (qsd) is a probability measure \nu on \Lambda that satisfies:…

We show that the quasi-stationary distribution of the subcritical contact process on $\mathbb{Z}^d$ is unique. This is in contrast with other processes which also do not come down from infinity, like stable queues and Galton-Watson, and it…

Quasi-stationary distributions, as discussed by Darroch & Seneta (1965), have been used in biology to describe the steady state behaviour of population models which, while eventually certain to become extinct, nevertheless maintain an…

We study the long time behaviour of a Markov process evolving in $\mathbb{N}$ and conditioned not to hit 0. Assuming that the process comes back quickly from infinity, we prove that the process admits a unique quasi-stationary distribution…