Diffusion Processes

General diffusion processes as the limit of time-space Markov chains
In this paper we prove the convergence of the law of grid-valued random walks, which can be seen as time-space Markov chains, to the …
Alexis Anagnostakis, Antoine Lejay, 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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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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Impact of demography on extinction/fixation events
In this article we consider diffusion processes modeling the dynamics of multiple allelic proportions (with fixed and varying …
Camille Coron, Sylvie Méléard, 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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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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Uniform convergence of penalized time-inhomogeneous Markov processes
We provide a general criterion ensuring the exponential contraction of Feynman–Kac semi-groups of penalized processes. This criterion …
Nicolas Champagnat, 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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