On Lin's condition for products of random variables with joint singular distribution

TL;DR

This paper investigates Lin's condition, a criterion for moment determinacy, specifically for the product of random variables when their joint distribution is singular, expanding its applicability beyond absolutely continuous cases.

Contribution

It introduces the analysis of Lin's condition for products of random variables with singular joint distributions, a novel extension of existing results.

Findings

Lin's condition can be applied to singular joint distributions

Product of random variables with singular joint distribution can satisfy Lin's condition

New criteria for moment determinacy in singular cases are proposed

Abstract

Lin's condition is used to establish the moment determinacy/indeterminacy of absolutely continuous probability distributions. Recently, a number of papers related to Lin's condition for functions of random variables have emerged. In this work, Lin's condition is studied for the product of random variables with given densities in the case when their joint distribution is singular.