Weighted Csiszár-kullback-pinsker Inequalities and Applications to Transportation Inequalities
نویسندگان
چکیده
Abstract. We strengthen the usual Csiszár-Kullback-Pinsker inequality by allowing weights in the total variation norm; admissible weights depend on the decay of the reference probability measure. We use this result to derive transportation inequalities involving Wasserstein distances for various exponents: in particular, we recover the equivalence between a T1 inequality and the existence of a square-exponential moment. Then we give a variant of the results obtained by Djellout, Guillin and Wu [5] about transportation inequalities for random dynamical systems, in which a sufficient condition is expressed in terms of exponential moments. A result by Blower [1] about the perturbation of a T2 inequality is also recovered and generalized.
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