A converse Poincarà e-type inequality is obtained within the class of smooth convex functions for the Gaussian distribution.
Converse Poincaré-type inequalities for convex functions
✍ Scribed by S.G. Bobkov; C. Houdré
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 264 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0167-7152
No coin nor oath required. For personal study only.
✦ Synopsis
Converse Poincarr-type inequalities are obtained within the class of smooth convex functions. This is, in particular, applied to the double exponential distribution.
📜 SIMILAR VOLUMES
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,
Many converses of Jensen's inequality for convex functions can be found in the literature. Here we give matrix versions, with matrix weights, of these inequalities. Some applications to the Hadamard product of matrices are also given. ᮊ 1997