Geodesic
Convex algebras of probability distributions induced by finite associative rings
Diskretnaya Matematika, Tome 31 (2019) no. 1, pp. 133-142.

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We consider the transformations of random variables over a finite associative ring by the addition and multiplication operations. For arbitrary finite rings, we construct families of distribution algebras, which are sets of distributions closed over sums and products of independent random variables.
Keywords: random variable, finite ring, discrete probability distribution, algebra. 
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A. D. Yashunskii. Convex algebras of probability distributions induced by finite associative rings. Diskretnaya Matematika, Tome 31 (2019) no. 1, pp. 133-142. http://geodesic.mathdoc.fr/item/DM_2019_31_1_a8/

[1] Kolpakov R. M., “Zamknutye klassy konechnykh raspredelenii ratsionalnykh veroyatnostei”, Diskretn. analiz i issled. oper., ser. 1, 11:3 (2004), 16–31 | MR

[2] Mal'cev A. I., Algebraic Systems, Springer-Verlag Berlin Heidelberg, 1973, 320 pp. | MR

[3] Salimov F. I., “Ob odnoi sisteme obrazuyuschikh dlya algebr nad sluchainymi velichinami”, Izv. vuzov. Matem., 1981, no. 5, 78–82 | Zbl

[4] Yashunsky A. D., “On read-once transformations of random variables over finite fields”, Discrete Math. Appl., 25:5 (2015), 311–321 | DOI | DOI | MR | Zbl

[5] Yashunskii A. D., “Convex polyhedra of distributions preserved by operations over a finite field”, Moscow Univ. Math. Bull., 72:4 (2017), 165–168 | DOI | MR | Zbl

[6] Lee D., Bruck J., “Generating probability distributions using multivalued stochastic relay circuits”, IEEE ISIT, 2011, 308–312