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Rate of convergence for ergodic continuous Markov processes : Lyapunov versus Poincaré
We study the relationship between two classical approaches for quantitative ergodic properties : the first one based on Lyapunov type controls and popularized by Meyn and Tweedie, the second oneExpand
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Quasi-stationary distributions and diffusion models in population dynamics
In this paper, we study quasi-stationarity for a large class of Kolmogorov diffusions. The main novelty here is that we allow the drift to go to $- \infty$ at the origin, and the diffusion to have anExpand
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Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry
We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations with general F-Sobolev inequalities, thus extending Gross hypercontractivity theory. We provideExpand
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A simple proof of the Poincaré inequality for a large class of probability measures
Abstract. We give a simple and direct proof of the existence of a spectral gap under some Lyapunov type condition which is satisfied in particular by log-concave probability measures onExpand
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Probabilistic approach for granular media equations in the non-uniformly convex case
We use here a particle system to prove both a convergence result (with convergence rate) and a deviation inequality for solutions of granular media equation when the confinement potential and theExpand
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Competitive or weak cooperative stochastic Lotka–Volterra systems conditioned on non-extinction
We are interested in the long time behavior of a two-type density-dependent biological population conditioned on non-extinction, in both cases of competition or weak cooperation between the twoExpand
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Hypoelliptic non-homogeneous diffusions
Abstract. Let be a time dependent second order operator, written in usual or Hörmander form. We study the regularity of the law of the associated non-homogeneous (time dependent) diffusion process,Expand
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In this paper we derive non asymptotic deviation bounds for P� � � � 1 Z t 0 V (X s)ds Z V dµ � � � R � where X is a µ stationary and ergodic Markov process and V is some µ integrable function. TheseExpand
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On quadratic transportation cost inequalities
Abstract In this paper we study quadratic transportation cost inequalities. To this end we introduce new families of inequalities (for quadratic transportation cost and for relative entropy) that areExpand
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Large deviations and Nelson processes
We obtain a large deviation principle for the empirical process of a large dynamical stochastic System of non-interacting particles. A careful study of the rate function of this large deviationExpand
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