By direct calculus we identify explicitly the Lipschitzian norm of the solution of the Poisson equation $-\mathcal{L}G=g$ in terms of various norms of g, where $\mathcal{L}$ 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 L1-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 examples.
Publié le : 2011-05-15
Classification:
Poisson equations,
Transportation–information inequalities,
Concentration and isoperimetric inequalities,
47B38,
60E15,
60J60,
34L15,
35P15
@article{1300887277,
author = {Djellout, Hacene and Wu, Liming},
title = {Lipschitzian norm estimate of one-dimensional Poisson equations and applications},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {47},
number = {1},
year = {2011},
pages = { 450-465},
language = {en},
url = {http://dml.mathdoc.fr/item/1300887277}
}
Djellout, Hacene; Wu, Liming. Lipschitzian norm estimate of one-dimensional Poisson equations and applications. Ann. Inst. H. Poincaré Probab. Statist., Tome 47 (2011) no. 1, pp. 450-465. http://gdmltest.u-ga.fr/item/1300887277/