Lyapunov criteria for uniform convergence of conditional distributions of absorbed Markov processes

By Nicolas Champagnat, Denis Villemonais. Stochastic Processes and their Applications, 2017

48 citations recorded by the source corpus.

We study the quasi-stationary behavior of multidimensional processes absorbed when one of the coordinates vanishes. Our results cover competitive or weakly cooperative Lotka-Volterra birth and death processes and Feller diffusions with competitive Lotka-Volterra interaction. To this aim, we develop original non-linear Lyapunov criteria involving two Lyapunov functions, which apply to general Markov processes.

Subfields: Public Health, Environmental and Occupational Health, Sociology and Political Science, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6e12e6756cc4866846bbacd37a01c6cfe53a98e1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Public Health, Environmental and Occupational Health

1. Nicolas Champagnat
2. Denis Villemonais
3. Amaury Lambert
4. S. M'el'eard

In Sociology and Political Science

1. Denis Villemonais
2. Nicolas Champagnat
3. Amaury Lambert
4. S. M'el'eard

In Statistical and Nonlinear Physics

1. Nicolas Champagnat
2. Denis Villemonais

Citations in the corpus

• General criteria for the study of quasi-stationarity (2017, methodology): “Compared to the results of [18] on Feller diffusions, our criterion covers weakly cooperative cases as in [10], i.”