$L_1$-norm of combinations of products of independent random variables

TL;DR

This paper demonstrates that the L1-norm of linear combinations of products of i.i.d. nonnegative mean-one random variables is proportional to the l1-norm of the coefficients, revealing a fundamental norm equivalence.

Contribution

It establishes a new norm equivalence result for combinations of products of independent random variables, extending understanding of their behavior.

Findings

L1-norm of combinations is comparable to l1-norm of coefficients

Results hold for products of i.i.d. nonnegative mean-one variables

Provides a fundamental norm equivalence in probabilistic analysis

Abstract

We show that $L_1$-norm of linear combinations (with scalar or vector coefficients) of products of i.i.d. nonnegative mean one random variables is comparable to $l_1$-norm of coefficients.