On contraction properties of Markov kernels
成果类型：
Article
署名作者：
Del Moral, P; Ledoux, M; Miclo, L
署名单位：
Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-003-0270-6
发表日期：
2003
页码：
395-420
关键词：
摘要：
We study Lipschitz contraction properties of general Markov kernels seen as operators on spaces of probability measures equipped with entropy-like distances''. Universal quantitative bounds on the associated ergodic constants are deduced from Dobrushin's ergodic coefficient. Strong contraction properties in Orlicz spaces for relative densities are proved under more restrictive mixing assumptions. We also describe contraction bounds in the entropy sense around arbitrary probability measures by introducing a suitable Dirichlet form and the corresponding modified logarithmic Sobolev constants. The interest in these bounds is illustrated on the example of inhomogeneous Gaussian chains. In particular, the existence of an invariant measure is not required in general.