Geodesic
On Lin's condition for products of random variables
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 15 (2019) no. 1, pp. 79-85 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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 Also, it is shown that without the condition of independence, the statement is no longer valid. 
@article{JMAG_2019_15_1_a2,
     author = {Alexander Il'inskii and Sofiya Ostrovska},
     title = {On {Lin's} condition for products of random variables},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {79--85},
     year = {2019},
     volume = {15},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2019_15_1_a2/}
}
TY  - JOUR
AU  - Alexander Il'inskii
AU  - Sofiya Ostrovska
TI  - On Lin's condition for products of random variables
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2019
SP  - 79
EP  - 85
VL  - 15
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JMAG_2019_15_1_a2/
LA  - en
ID  - JMAG_2019_15_1_a2
ER  - 
%0 Journal Article
%A Alexander Il'inskii
%A Sofiya Ostrovska
%T On Lin's condition for products of random variables
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2019
%P 79-85
%V 15
%N 1
%U http://geodesic.mathdoc.fr/item/JMAG_2019_15_1_a2/
%G en
%F JMAG_2019_15_1_a2
Alexander Il'inskii; Sofiya Ostrovska. On Lin's condition for products of random variables. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 15 (2019) no. 1, pp. 79-85. http://geodesic.mathdoc.fr/item/JMAG_2019_15_1_a2/

[1] P. Kopanov, J. Stoyanov, “Lin's condition for functions of random variables and moment determinacy of probability distributions”, C. R. Acad. Bulgare Sci., 70:5 (2017), 611–618 | MR | Zbl

[2] G.A. Korn, Th.M. Korn, Mathematical Handbook for Scientists and Engineers, 2nd ed., McGraw-Hill Book Co., New York–Toronto, Ont.–London, 1968 | MR

[3] G.D. Lin, “On the moment problems”, Stat. Prob. Lett., 35 (1997), 85–90 | DOI | MR | Zbl

[4] G.D. Lin, “Recent developments on the moment problem”, J. Statist. Dist. Appl., 4:5 (2017) | DOI

[5] S. Ostrovska, M. Turan, “On the powers of Kummer distribution”, Kuwait J. Sci., 44:2 (2017), 1–8 | MR | Zbl

[6] D. Stirzaker, The Cambridge Dictionary of Probability and its Applications, Cambridge University Press, Cambridge, 2015 | MR | Zbl

[7] J. Stoyanov, Counterexamples in Probability, 3rd ed., Dover Publications, Inc., Mineola, NY, 2013 | MR | Zbl

[8] J. Stoyanov, “Krein condition in probabilistic moment problems”, Bernoulli, 6:5 (2000), 939–949 | DOI | MR | Zbl

[9] J. Stoyanov, P. Kopanov, Lin's condition and moment determinacy of functions of random variables, preprint