Geodesic
Properties of stochastic operators of order $\nu$ on a finite-dimensional simplex
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 166 (2024) no. 4, pp. 651-659 Cet article a éte moissonné depuis la source Math-Net.Ru

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The necessary and sufficient conditions for stochasticity and bistochasticity of positive operators were analyzed. Key criteria for stochasticity of continuous positive operators in $\mathbb{R}^{m}$ were proved. The necessary and sufficient condition for these operators to be referred to as bistochastic was established.
Keywords: stochastic operator, bistochastic operator, cone, positive operator, rearrangements of cone element. 
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Yu. Kh. Èshkabilov; J. Z. Istamov. Properties of stochastic operators of order $\nu$ on a finite-dimensional simplex. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 166 (2024) no. 4, pp. 651-659. http://geodesic.mathdoc.fr/item/UZKU_2024_166_4_a13/

[1] Bernstein S.N., “Solution of a mathematical problem connected with the theory of heredity”, Ann. Math. Stat., 13:1 (1942), 53–61

[2] Ulam S., A Collection of Mathematical Problems, Nauka, M., 1964, 168 pp. (In Russian)

[3] Vallander S.S., “On the limit behavior of iteration sequences of certain quadratic transformations”, Dokl. Akad. Nauk SSSR, 202:3 (1972), 515–517 (In Russian)

[4] Lyubich Yu.I., Mathematical Structures in Population Genetics, Naukova Dumka, Kyiv, 1983, 296 pp. (In Russian)

[5] Ganikhodzhaev R.N. Quadratic stochastic operators, Lyapunov functions, and tournaments, Sb.: Math., 76:2 (1993), 489–506 | DOI

[6] Ganikhodzhaev R.N. On the definition of bistochastic quadratic operators, Russ. Math. Surv., 48:4 (1993), 244–246 | DOI

[7] Rozikov U.A., Khamraev A.Yu., “On cubic operators defined on finite-dimensional simplexes”, Ukr. Math. J., 56:10 (2004), 1699–1711 | DOI

[8] Shahidi F., “On the extreme points of the set of bistochastic operators”, Math. Notes, 84:3 (2008), 442–448 | DOI

[9] Ganikhodzhaev R., Shahidi F., “Doubly stochastic quadratic operators and Birkhoff's problem”, Linear Algebra Appl., 432:1 (2010), 24–35 | DOI

[10] Shahidi F.A., “On bistochastic operators defined on a finite-dimensional simplex”, Sib. Math. J., 50:2 (2009), 368–372 | DOI

[11] Marshall A.W., Olkin I., Inequalities: Theory of Majorization and Its Applications, Mir, M., 1983, 574 pp. (In Russian)