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Contents of PMS, Vol. 40, Fasc. 1,
pages 97 - 104
DOI: 10.37190/0208-4147.40.1.6
Published online 2.4.2020
 

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

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