A note on the invariance principle of the product of sums of random variables

TL;DR

This paper demonstrates that the central limit theorems for the product of sums of random variables can be derived as a corollary of the invariance principle, linking these results in probability theory.

Contribution

It establishes that the invariance principle underpins the central limit theorems for the product of sums of random variables, providing a unified theoretical framework.

Findings

Central limit theorems for product of sums follow from the invariance principle.

The invariance principle offers a foundational basis for these limit theorems.

The results unify previous disparate findings in probability theory.

Abstract

In literature, the central limit theorems for the product of sums of various random variables have studied. The purpose of this note is to show that this kind of results are corollary of the invariance principle.