Browsing by Author "Il'inskii, Alexander"

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Citation - WoS: 1
On Lin's Condition for Products of Random Variables
(B verkin inst Low Temperature Physics & Engineering Nas Ukraine, 2019) Il'inskii, Alexander; Ostrovska, Sofiya; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
The paper presents an elaboration of some results on Lin's conditions. A new proof is given to the fact that if densities of independent random variables xi(1) and xi(2) satisfy Lin's condition, then the same is true for their product. Also, it is shown that without the condition of independence, the statement is no longer valid.
Citation - WoS: 1
Citation - Scopus: 1
On Lin's Condition for Products of Random Variables With Singular Joint Distribution
(Wydawnictwo Uniwersytetu Wroclawskiego, 2020) Il'inskii, Alexander; Ostrovska, Sofiya; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
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.