Convex algebras of probability distributions induced by finite associative rings-Reference-Cited by-同舟云学术

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Convex algebras of probability distributions induced by finite associative rings

Published:2021-06-01 Issue:3 Volume:31 Page:223-230
ISSN:0924-9265
Container-title:Discrete Mathematics and Applications
language:en
Short-container-title:

Author:

Yashunsky Alexey D.¹

Affiliation:

1. Keldysh Institute of Applied Mathematics of Russian Academy of Sciences , Moscow , Russia

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics

Link

https://www.degruyter.com/document/doi/10.1515/dma-2021-0019/pdf

Reference6 articles.

1. R. M. Kolpakov, “Closed classes of finite distributions of rational probabilities”, Diskretn. Anal. Issled. Oper., Ser. 1,11:3 (2004), 16-31.

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

3. F. I. Salimov, “On a system of generators for algebras over random variables”, Izv. Vyssh. Uchebn. Zaved. Mat., 1981, N 5, 78-82.

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

5. Yashunskii A. D., “Convex polyhedra of distributions preserved by operations over a finite field”, Moscow Univ. Math. Bull., 72:4 (2017), 165-168.

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