Displaying similar documents to “Transportation inequalities for stochastic differential equations of pure jumps”

Lipschitzian norm estimate of one-dimensional Poisson equations and applications

Hacene Djellout, Liming Wu (2011)

Annales de l'I.H.P. Probabilités et statistiques

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By direct calculus we identify explicitly the lipschitzian norm of the solution of the Poisson equation in terms of various norms of , where is a Sturm–Liouville operator or generator of a non-singular diffusion in an interval. This allows us to obtain the best constant in the 1-Poincaré inequality (a little stronger than the Cheeger isoperimetric inequality) and some sharp transportation–information inequalities and concentration inequalities for empirical means. We conclude with several...

Poincaré inequalities and dimension free concentration of measure

Nathael Gozlan (2010)

Annales de l'I.H.P. Probabilités et statistiques

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In this paper, we consider Poincaré inequalities for non-euclidean metrics on ℝ. These inequalities enable us to derive precise dimension free concentration inequalities for product measures. This technique is appropriate for a large scope of concentration rate: between exponential and gaussian and beyond. We give equivalent functional forms of these Poincaré type inequalities in terms of transportation-cost inequalities and inf-convolution inequalities. Workable sufficient conditions...

Exponential concentration for first passage percolation through modified Poincaré inequalities

Michel Benaïm, Raphaël Rossignol (2008)

Annales de l'I.H.P. Probabilités et statistiques

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We provide a new exponential concentration inequality for first passage percolation valid for a wide class of edge times distributions. This improves and extends a result by Benjamini, Kalai and Schramm ( (2003)) which gave a variance bound for Bernoulli edge times. Our approach is based on some functional inequalities extending the work of Rossignol ( (2006)), Falik and Samorodnitsky ( (2007)).

Trends to equilibrium in total variation distance

Patrick Cattiaux, Arnaud Guillin (2009)

Annales de l'I.H.P. Probabilités et statistiques

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This paper presents different approaches, based on functional inequalities, to study the speed of convergence in total variation distance of ergodic diffusion processes with initial law satisfying a given integrability condition. To this end, we give a general upper bound “à la Pinsker” enabling us to study our problem firstly via usual functional inequalities (Poincaré inequality, weak Poincaré,…) and truncation procedure, and secondly through the introduction of new functional inequalities...