Transportation-information inequalities for Markov processes - Guillin, Arnaud; Léonard, Christian; Wu, Liming; Yao, Nian (Probability theory and related fields, 2009)
In this paper, one investigates the transportation-information T c I inequalities: α ( T c ( ν, μ )) ≤ I ( ν | μ ) for all probability measures ν on a metric space , where μ is a given probability measure, T c ( ν, μ ) is the transportation cost from ν to μ with respect to the cost function c ( x , y ) on , I ( ν | μ ) is the Fisher–Donsker–Varadhan information of ν with respect to μ and α : [0, ∞) → [0, ∞] is a left continuous increasing function. Using large deviation techniques, it is shown that T c I is equivalent to some concentration inequality for the occupation measure of a μ -reversible ergodic Markov process related to I (·| μ ). The tensorization property of T c I and comparisons of T c I with Poincaré and log-Sobolev inequalities are investigated. Several easy-to-check sufficient conditions are provided for special important cases of T c I and several examples are worked out.