Tail estimates for random variables from interrelation between corresponding moments inequalities

TL;DR

This paper develops tail inequalities for random variables based on their moment and Lebesgue-Riesz norm inequalities, with applications to martingale theory, providing a new method to estimate tail behavior from moment relations.

Contribution

It introduces a novel approach to derive tail bounds from moment inequalities, extending existing techniques to broader parameter sets and applications in martingale theory.

Findings

Derived tail inequalities from moment and norm inequalities.

Applied the inequalities to martingale theory.

Extended the parameter ranges for tail estimates.

Abstract

We derive the tail inequalities between two random variables starting from inequalities between its moment, or more generally between its Lebesgue-Riesz norms, which holds true on certain sets of parameters. We consider some applications into the martingale theory.