Population Models

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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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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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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