| Université Paul Sabatier | Toulouse | |
| CNRS U.M.R. C5583 | ||
| Laboratoire de Statistique et Probabilités | ||
Auteur(s): P. Del Moral, M. Ledoux et L. Miclo
Code(s) de Classification MSC:
Résumé: We study Lipschitz's contraction properties of general Markovian kernels seen as operators on spaces of probabilities endowed with entropy-like ``distances". Universal quantitative bounds on the associated ergodic constants are deduced from Dobrushin's coefficient and strong contraction properties in Orlicz's spaces for relative densities are proved under restrictive mixing assumptions. Next we obtain contraction estimates in the entropy sense around an arbitrary probability by introducing a particular Dirichlet form and the corresponding modified logarithmic Sobolev inequalities. The interest of these bounds will be illustred by inhomogeneous Gaussian examples, emphasizing the irrelevence of the existence of an invariant measure assumption.
Mots Clés: Lipschitz's contraction, generalized relative entropy, Markov kernel, Dobrushin's coefficient, Orlicz's norm for densities, appropriate Dirichlet form, spectral gap, modified logarithmic Sobolev inequality, loose of memory property for inhomogeneous Gaussian chains.
Date: 2001-02-05
Prépublication numéro:
LSP-2001-01