We obtain a closed-form formula for the quasi-stationary distribution of the classical Shiryaev martingale diffusion considered on the positive half-line [A, +∞) withA>0 fixed; the state space’s left endpoint is assumed ...

We show that the quasi-stationary distribution of the subcritical contact process on Zd is unique. This is in contrast with other processes which also do not come down from infinity, like stable queues and Galton-Watson, ...

In this paper we study quasi-stationarity for a large class of Kolmogorov diffusions. The main novelty here is that we allow the drift to go to−∞at the origin, and the diffusion to have an entrance boundary at +∞. These ...

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 ...

Consider N particles moving independently, each one according to a subcritical continuous-time Galton-Watson process unless it hits 0, at which time it jumps instantaneously to the position of one of the other particles ...

Quasi-stationary distributions (QSD) have been widely studied since the pioneering work of Kolmogorov (1938), Yaglom (1947) and Sevastyanov (1951). They appear as a natural object when considering Markov processes that are ...

We jointly investigate the existence of quasi-stationary distributions for one dimensional Lévy processes and the existence of traveling waves for the Fisher-Kolmogorov-Petrovskii-Piskunov (F-KPP) equation associated with ...

Consider a continuous-time Markov process with transition rates matrix Q in the state space Λ ⋃ {0}. In the associated Fleming-Viot process N particles evolve independently in Λ with transition rates matrix Q until one of ...

We analyze the connection between front propagation and quasi-stationary distributions in translation invariant one-dimensional Markov processes. We describe the link between them through the microscopic models known as ...