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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2018, Volume 301, Pages 320–335
DOI: https://doi.org/10.1134/S037196851802022X (Mi tm3910) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Algebras of probability distributions on finite sets

A. D. Yashunsky

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047 Russia
Full-text PDF (280 kB) Citations (11)
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DOI: https://doi.org/10.1134/S037196851802022X
Abstract: We consider the problems of transforming random variables over finite sets by discrete functions. We describe the problems of exact and approximate expression of random variables as functions of other random variables from the point of view of universal algebra and provide a review of results in the area. Sufficient conditions are obtained for a system of transforming functions to allow the approximation of an arbitrary probability distribution on a finite set using a given nondegenerate initial distribution.
Funding agency Grant number
Russian Science Foundation 14-21-00025
This work is supported by the Russian Science Foundation under grant 14-21-00025.
Received: October 9, 2017
English version:
Proceedings of the Steklov Institute of Mathematics, 2018, Volume 301, Pages 304–318
DOI: https://doi.org/10.1134/S0081543818040223
Bibliographic databases:
Document Type: Article
UDC: 519.7+512.57+519.213
Language: Russian
Citation: A. D. Yashunsky, “Algebras of probability distributions on finite sets”, Complex analysis, mathematical physics, and applications, Collected papers, Trudy Mat. Inst. Steklova, 301, MAIK Nauka/Interperiodica, Moscow, 2018, 320–335; Proc. Steklov Inst. Math., 301 (2018), 304–318
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    1. E. E. Trifonova, “O bespovtorno zamknutykh klassakh bulevykh funktsii, indutsiruyuschikh nekotorye preobrazovaniya ratsionalnykh veroyatnostei”, Diskret. matem., 37:1 (2025), 119–129  mathnet  crossref
    2. E. E. Trifonova, “O chisle p-sokratimykh indutsirovannykh veroyatnostnykh funktsii”, Intellektualnye sistemy. Teoriya i prilozheniya, 27:1 (2023), 134–142  mathnet
    3. A. D. Yashunskii, “On Sums of Bernoulli Random Variables Modulo 3”, Math. Notes, 111:1 (2022), 166–169  mathnet  crossref  crossref  mathscinet  isi
    4. E. E. Trifonova, “O nekotorykh svoistvakh konechno porozhdayuschikh sistem preobrazovatelei p-ichnykh drobei”, Diskretn. analiz i issled. oper., 29:4 (2022), 124–135  mathnet  crossref  mathscinet
    5. E. E. Trifonova, “O nekotorykh svoistvakh konechno porozhdayuschikh sistem preobrazovatelei p-ichnykh drobei”, Material konferentsii: “XIV mezhdunarodnyi nauchnyi seminar "Diskretnaya matematika i ee prilozheniya” imeni akademika O.B. Lupanova (20-25 iyunya 2022 g., Moskva), Proceedings of Academician O.B. Lupanov 14th International Scientific Seminar “Discrete Mathematics and Its Applications”, 2022, 138–141  crossref
    6. E. E. Trifonova, “On some properties of finitely generating transformer sets for p-ary fractions”, J. Appl. Ind. Math., 16:4 (2022), 834  crossref  mathscinet
    7. A. D. Yashunskii, “O preobrazovaniyakh trekhznachnykh sluchainykh velichin funktsiyami dvukh peremennykh”, Diskretn. analiz i issled. oper., 28:3 (2021), 90–103  mathnet  crossref
    8. E. E. Trifonova, “O beskonechnoi porozhdennosti pyaterichnykh drobei v odnom klasse preobrazovatelei veroyatnostei”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2021, no. 1, 39–48  mathnet  crossref
    9. A. D. Yashunsky, “On Transformations of Three-Valued Random Variables by Bivariate Functions”, J. Appl. Ind. Math., 15:3 (2021), 558  crossref  mathscinet
    10. A. D. Yashunsky, “On the approximation of random variables on a finite chain”, J. Appl. Industr. Math., 14:3 (2020), 581–591  mathnet  crossref  crossref
    11. A. D. Yashunsky, “Limit points of Bernoulli distribution algebras induced by boolean functions”, Lobachevskii J. Math., 40:9, SI (2019), 1423–1432  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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