Moment and Tail Inequalities for Polynomial Martingales

TL;DR

This paper derives precise non-asymptotic moment and tail bounds for polynomial functions of martingale differences, providing examples to demonstrate the accuracy of these estimates.

Contribution

It introduces exact non-asymptotic moment and tail inequalities specifically for polynomial martingales, advancing the understanding of their probabilistic behavior.

Findings

Exact moment estimates for polynomial martingales

Precise tail bounds established

Examples confirming the sharpness of results

Abstract

In this paper we obtain the non-asymptotic exact moment and tails estimates for polynomial on martingale differences. We give also some examples on order to show the exactness of obtained results.