This paper introduces a new kind of modified transportation cost inequalities and presents some sufficient and necessary conditions for it. Using these conditions, this paper provides some applications of polynomial concentration inequalities to probability measures with no exponential moments....

In this paper, we study Wasserstein-Divergence transportation inequalities which are the generalization of classical transportation inequalities. We present sufficient and necessary conditions for them separately, which coincide in the limit case. Using this kind of inequalities, we establish...

In this paper, we study the quadratic transportation and divergence inequality, which is the generalization of Talagrand’s transportation inequality. We obtain its tensorization property, prove it is implied by Poincaré inequality, and give a criterion for it.

An identity found by Müller (Ann. Inst. Statist. Math. 53 (2001) 567) for normal distributions is generalized to Kotz-type distributions. Some stochastic orders of Kotz-type distributions are discussed by means of this identity.