Some notes on moment inequalities for heavy-tailed distributions

Abstract

We investigate the relation between moments and tails of heavy-tailed (in particular, Pareto-type) distributions. We also discuss the sharpness of our results in a number of examples under certain regularity conditions like log-convexity. Moreover, we derive concentration bounds for polynomial chaos of any order $d$.

Final version as to be published in HDP X, including a number of further modifications and corrections