Tails of Polynomials of Random Variables and Stable Limits for Nonconventional Sums

TL;DR

This paper investigates the tail behavior of polynomials of independent heavy-tailed random variables and establishes stable limit theorems for nonconventional sums involving these polynomials.

Contribution

It provides new decay rate estimates for tail probabilities and proves stable limit theorems for sums of polynomial functions of heavy-tailed variables.

Findings

Decay rates for tail probabilities of polynomial functions

Stable limit theorems for nonconventional sums

Applicable to heavy-tailed independent random variables

Abstract

We obtain decay rates of probabilities of tails of polynomials in several independent random variables with heavy tails and derive stable limit theorems for nonconventional sums of such polynomials