Quasi-Stationary Distribution

Binary branching processes with Moran type interactions
The aim of this paper is to study the large population limit of a binary branching particle system with Moran type interactions. We …
Alexander Cox, Emma Horton, Denis Villemonais
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Lyapunov criteria for uniform convergence of conditional distributions of absorbed Markov processes
We study the quasi-stationary behavior of multidimensional processes absorbed when one of the coordinates vanishes. Our results cover …
Nicolas Champagnat, Denis Villemonais
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Stochastic approximation of quasi-stationary distributions for diffusion processes in a bounded domain
We study a random process with reinforcement, which evolves following the dynamics of a given diffusion process in a bounded domain and …
Michel Benaïm, Nicolas Champagnat, Denis Villemonais
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Convergence of the Fleming-Viot process toward the minimal quasi-stationary distribution
We prove under mild conditions that the Fleming-Viot process selects the minimal quasi-stationary distribution for Markov processes …
Nicolas Champagnat, Denis Villemonais
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Lower Bound for the Coarse Ricci Curvature of Continuous-Time Pure-Jump Processes
We obtain a lower bound for the coarse Ricci curvature of continuous-time pure-jump Markov processes, with an emphasis on interacting …
Denis Villemonais
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Practical criteria for R-positive recurrence of unbounded semigroups
The goal of this note is to show how recent results on the theory of quasi-stationary distributions allow to deduce effortlessly …
Nicolas Champagnat, Denis Villemonais
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Exponential mixing properties for time inhomogeneous diffusion processes with killing
We consider an elliptic and time-inhomogeneous diffusion process with time-periodic coefficients evolving in a bounded domain of …
Pierre Del Moral, Denis Villemonais
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Convergence of a non-failable mean-field particle system
The existing literature contains many examples of mean-field particle systems converging to the distribution of a Markov process …
William Oçafrain, Denis Villemonais
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Exponential convergence to quasi-stationary distribution for absorbed one-dimensional diffusions with killing
This article studies the quasi-stationary behavior of absorbed one-dimensional diffusion processes with killing on $[0,\infty)$. We …
Nicolas Champagnat, Denis Villemonais
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Uniform convergence of conditional distributions for absorbed one-dimensional diffusions
In this paper we study the quasi-stationary behavior of absorbed one-dimensional diffusions. We obtain necessary and sufficient …
Nicolas Champagnat, Denis Villemonais
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Uniform convergence to the $Q$-process
The first aim of the present note is to quantify the speed of convergence of a conditioned process toward its $Q$-process under …
Nicolas Champagnat, Denis Villemonais
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Population processes with unbounded extinction rate conditioned to non-extinction
This article studies the quasi-stationary behaviour of population processes with unbounded absorption rate, including one-dimensional …
Nicolas Champagnat, Denis Villemonais
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Exponential convergence to quasi-stationary distribution and $Q$-process
For general, almost surely absorbed Markov processes, we obtain necessary and sufficient conditions for exponential convergence to a …
Nicolas Champagnat, Denis Villemonais
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Quasi-stationary distribution for multi-dimensional birth and death processes conditioned to survival of all coordinates
This article studies the quasi-stationary behaviour of multidimensional birth and death processes, modeling the interaction between …
Nicolas Champagnat, Denis Villemonais
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Minimal quasi-stationary distribution approximation for a birth and death process
In a first part, we prove a Lyapunov-type criterion for the $\xi_1$-positive recurrence of absorbed birth and death processes and …
Denis Villemonais
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Existence and Uniqueness of a Quasistationary Distribution for Markov Processes with Fast Return from Infinity
We study the long-time behaviour of a Markov process evolving in $\mathbb{N}$ and conditioned not to hit 0. Assuming that the process …
Servet Martínez, Jaim San Martín, Denis Villemonais
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Quasi-stationary distributions and population processes
This survey concerns the study of quasi-stationary distributions with a specific focus on models derived from ecology and population …
Sylvie Méléard, Denis Villemonais
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Interacting Particle Systems and Yaglom Limit Approximation of Diffusions with Unbounded Drift
We study the existence and the exponential ergodicity of a general interacting particle system, whose components are driven by …
Denis Villemonais
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Approximation of quasi-stationary distributions for 1-dimensional killed diffusions with unbounded drifts
The long time behavior of an absorbed Markov process is well described by the limiting distribution of the process conditioned to not …
Denis Villemonais
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