Weighted Csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities

Weighted Csiszár-kullback-pinsker Inequalities and Applications to Transportation Inequalities

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 ...

On Reverse Pinsker Inequalities

New upper bounds on the relative entropy are derived as a function of the total variation distance. One bound refines an inequality by Verdú for general probability measures. A second bound improves the tightness of an inequality by Csiszár and Talata for arbitrary probability measures that are defined on a common finite set. The latter result is further extended, for probability measures on a ...

Generalised Pinsker Inequalities

We generalise the classical Pinsker inequality which relates variational divergence to Kullback-Liebler divergence in two ways: we consider arbitrary f -divergences in place of KL divergence, and we assume knowledge of a sequence of values of generalised variational divergences. We then develop a best possible inequality for this doubly generalised situation. Specialising our result to the clas...

Modified logarithmic Sobolev inequalities and transportation inequalities

Some extended Simpson-type inequalities and applications

‎In this paper‎, ‎we shall establish some extended Simpson-type inequalities‎ ‎for differentiable convex functions and differentiable concave functions‎ ‎which are connected with Hermite-Hadamard inequality‎. ‎Some error estimates‎ ‎for the midpoint‎, ‎trapezoidal and Simpson formula are also given‎.