Displaying similar documents to “Lipschitzian norm estimate of one-dimensional Poisson equations and applications”

Transportation inequalities for stochastic differential equations of pure jumps

Liming Wu (2010)

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

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For stochastic differential equations of pure jumps, though the Poincaré inequality does not hold in general, we show that 1 transportation inequalities hold for its invariant probability measure and for its process-level law on right continuous paths space in the 1-metric or in uniform metrics, under the dissipative condition. Several applications to concentration inequalities are given.

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...