On Lin's condition for products of random variables with
singular joint distribution
A. Il'inskii
S. Ostrovska
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 appeared.
In the present paper, this condition is studied for products of random variables with
given densities in the case when their joint distribution is singular. It is proved,
assuming that the densities of both random variables satisfy Lin’s condition,
that the density of their product may or may not satisfy this condition.
2010 AMS Mathematics Subject Classification: Primary 60E05; Secondary 44A60.
Keywords and phrases: random variable, singular distribution, Lin's condition