On a probabilistic Bernstein model
Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 2, pp. 392-401 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Extensions of S. N. Bernstein's example of three dependent random events of which any two are independent are considered. A complete description of such examples is given in the framework of the symmetric probability model.
Keywords: Bernstein example, dependent (independent) random events, $j$-free number.
Mots-clés : Diophantine equation
@article{TVP_2021_66_2_a8,
     author = {A. I. Rubinshtein and V. B. Sherstyukov},
     title = {On a~probabilistic {Bernstein} model},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {392--401},
     year = {2021},
     volume = {66},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2021_66_2_a8/}
}
TY  - JOUR
AU  - A. I. Rubinshtein
AU  - V. B. Sherstyukov
TI  - On a probabilistic Bernstein model
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2021
SP  - 392
EP  - 401
VL  - 66
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TVP_2021_66_2_a8/
LA  - ru
ID  - TVP_2021_66_2_a8
ER  - 
%0 Journal Article
%A A. I. Rubinshtein
%A V. B. Sherstyukov
%T On a probabilistic Bernstein model
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2021
%P 392-401
%V 66
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_2021_66_2_a8/
%G ru
%F TVP_2021_66_2_a8
A. I. Rubinshtein; V. B. Sherstyukov. On a probabilistic Bernstein model. Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 2, pp. 392-401. http://geodesic.mathdoc.fr/item/TVP_2021_66_2_a8/

[1] S. N. Bernshtein, Teoriya veroyatnostei, 4-e dop. izd., Gostekhizdat, M.–L., 1946, 556 pp.

[2] A. A. Borovkov, Probability theory, Gordon and Breach Sci. Publ., Amsterdam, 1998, x+474 pp. | MR | MR | Zbl

[3] B. W. Gnedenko, Einführung in die Wahrscheinlichkeitstheorie, Math. Lehrbücher Monogr. I. Abt. Math. Lehrbücher, 39, Akademie-Verlag, Berlin, 1991, 469 pp. | MR | Zbl

[4] G. J. Székély, Paradoxes in probability theory and mathematical statistics, Math. Appl. (East Eur. Ser.), 15, D. Reidel Publishing Co., Dordrecht, 1986, xii+250 pp. | MR | MR | Zbl | Zbl

[5] J. M. Stoyanov, Counterexamples in probability, Wiley Ser. Probab. Stat., 2nd ed., John Wiley Sons, Ltd., Chichester, 1997, xxviii+342 pp. | MR | Zbl | Zbl

[6] A. Granville, O. Ramaré, “Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients”, Mathematika, 43:1 (1996), 73–107 | DOI | MR | Zbl

[7] A. A. Bukhshtab, Teoriya chisel, 2-e ispr. izd., Prosveschenie, M., 1966, 384 pp. | MR | Zbl