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Transportation inequalities for stochastic differential equations of pure jumps

Liming Wu — 2010

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

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.

Lipschitzian norm estimate of one-dimensional Poisson equations and applications

Hacene DjelloutLiming Wu — 2011

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

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 illustrative...

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