Quasi-Stationary Distributions

Uniform Wasserstein convergence of penalized Markov processes
For general penalized Markov processes with soft killing, we propose a simple criterion ensuring uniform convergence of conditional …
Nicolas Champagnat, Edouard Strickler, Denis Villemonais
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Transcritical bifurcation for the conditional distribution of a diffusion process
In this article, we describe a simple class of models of absorbed diffusion processes with parameter, whose conditional law exhibits a …
Michel Benaïm, Nicolas Champagnat, William Oçafrain, Denis Villemonais
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General criteria for the study of quasi-stationarity
For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential non-uniform convergence in …
Nicolas Champagnat, Denis Villemonais
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Quasi-compactness criterion for strong Feller kernels with an application to quasi-stationary distributions
The aim of this note is to provide a sufficient criterion for the quasi-compactness of positive operators on $L^\infty$ type spaces. We …
Michel Benaïm, Nicolas Champagnat, William Oçafrain, Denis Villemonais
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A quasi-stationary approach to the long-term asymptotics of the growth-fragmentation equation
In a growth-fragmentation system, cells grow in size slowly and split apart at random. Typically, the number of cells in the system …
Denis Villemonais, Alexander Watson
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Quasi-stationary distributions in reducible state spaces
We study quasi-stationary distributions and quasi-limiting behavior of Markov chains in general reducible state spaces with absorption. …
Nicolas Champagnat, Denis Villemonais
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Degenerate processes killed at the boundary of a domain
We investigate certain properties of degenerate Feller processes that are killed when exiting a relatively compact set. Our main result …
Michel Benaïm, Nicolas Champagnat, William Oçafrain, Denis Villemonais
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Probabilistic Non-asymptotic Analysis of Distributed Algorithms
We present a new probabilistic analysis of distributed algorithms. Our approach relies on the theory of quasi-stationary distributions …
Nicolas Champagnat, René Schott, Denis Villemonais
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Stochastic approximation on non-compact measure spaces and application to measure-valued Pólya processes
Our main result is to prove almost-sure convergence of a stochastic-approximation algorithm defined on the space of measures on a …
Cécile Mailler, Denis Villemonais
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Exponential convergence to a quasi-stationary distribution and applications
This HDR is a reflection of my research since the end of my PhD thesis. It is also a presentation, in a more accessible form than in …
Denis Villemonais
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Criteria for Exponential Convergence to Quasi-Stationary Distributions and Applications to Multi-Dimensional Diffusions
We consider general Markov processes with absorption and provide criteria ensuring the exponential convergence in total variation of …
Nicolas Champagnat, Koléhé Coulibaly-Pasquier, Denis Villemonais
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Quasi-stationary distributions and particular methods for the approximation of conditioned processes
My PhD thesis focuses on the study of the distributions of stochastic processes with absorption and their approximation. This processes …
Denis Villemonais
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