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Capacitary Criteria for Poincaré-Type Inequalities

✍ Scribed by Mu-Fa Chen

Publisher
Springer Netherlands
Year
2005
Tongue
English
Weight
322 KB
Volume
23
Category
Article
ISSN
0926-2601

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Converse Poincarr-type inequalities are obtained within the class of smooth convex functions. This is, in particular, applied to the double exponential distribution.

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Using martingale techniques we will prove several deviation inequalities for diffusion processes in a compact Riemannian manifold and Le vy processes in euclidean space. We also deduce deviation inequalities from Poincare type inequalities in the abstract setting of Dirichlet forms. We thus obtain,