UNIVERSITY
OF WROCŁAW
 
Main Page
Contents
Online First
General Information
Instructions for authors


VOLUMES
43.2 43.1 42.2 42.1 41.2 41.1 40.2
40.1 39.2 39.1 38.2 38.1 37.2 37.1
36.2 36.1 35.2 35.1 34.2 34.1 33.2
33.1 32.2 32.1 31.2 31.1 30.2 30.1
29.2 29.1 28.2 28.1 27.2 27.1 26.2
26.1 25.2 25.1 24.2 24.1 23.2 23.1
22.2 22.1 21.2 21.1 20.2 20.1 19.2
19.1 18.2 18.1 17.2 17.1 16.2 16.1
15 14.2 14.1 13.2 13.1 12.2 12.1
11.2 11.1 10.2 10.1 9.2 9.1 8
7.2 7.1 6.2 6.1 5.2 5.1 4.2
4.1 3.2 3.1 2.2 2.1 1.2 1.1
 
 
WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

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

References


[1] A. Il'inskii and S. Ostrovska, On Lin’s condition for products of random variables, Zh. Mat. Fiz. Anal. Geom. 15 (2019), 79-85.

[2] P. Kopanov and J. Stoyanov, Lin’s condition for functions of random variables and moment determinacy of probability distributions, C. R. Acad. Bulgare Sci. 70 (2017), 611-618.

[3] G. D. Lin, On the moment problems, Statist. Probab. Lett. 35 (1997), 85-90.

[4] G. D. Lin, Recent developments on the moment problem, J. Statist. Distributions Appl. 4 (2017), 1-17.

[5] G. D. Lin and J. Stoyanov, Moment determinacy of powers and products of nonnegative random variables. J. Theoret. Probab. 28 (2015), 1337-1353.

[6] G. D. Lin and J. Stoyanov, On the moment determinacy of products of non-identically distributed random variables. Probab. Math. Statist. 36 (2016), 21-33.

[7] A.G. Pakes, Remarks on converse Carleman and Krein criteria for the classical moment problem, J. Austral. Math. Soc. 71 (2001), 81-104.

[8] D. Stirzaker, The Cambridge Dictionary of Probability and its Applications, Cambridge Univ. Press, 2015.

[9] J. Stoyanov, Counterexamples in Probability, 3rd ed., Dover Publ., New York, 2013.

[10] J. Stoyanov, Krein condition in probabilistic moment problems, Bernoulli 6 (2000), 939-949.

Download:    Abstract    Full text