Geodesic
On the approximation of random variables on~a~finite~chain
Diskretnyj analiz i issledovanie operacij, Tome 27 (2020) no. 3, pp. 109-125.

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We consider the transformations of independent random variables over a linearly ordered finite set (a chain) by the join and meet operations. We investigate the possibility of approximating an arbitrary probability distribution on a chain by means of a (possibly iterated) application of the join and meet operations to independent random variables with distributions from a given set. We establish some conditions under which the approximation is impossible and the conditions when it becomes possible. Illustr. 3, bibliogr. 9.
Mots-clés : finite chain, distribution
Keywords: linearly ordered set, random variable, approximation. 
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A. D. Yashunsky. On the approximation of random variables on~a~finite~chain. Diskretnyj analiz i issledovanie operacij, Tome 27 (2020) no. 3, pp. 109-125. http://geodesic.mathdoc.fr/item/DA_2020_27_3_a5/

[1] F. I. Salimov, “Finite generability of distribution algebras”, Diskretn. Anal. Issled. Oper., Ser. 1, 4:2 (1997), 43–50 (Russian) | MR | Zbl

[2] R. M. Kolpakov, “Closed classes of finite distributions of rational probabilities”, Diskretn. Anal. Issled. Oper., Ser. 1, 11:3 (2004), 16–31 (Russian) | MR

[3] A. D. Yashunsky, “Algebras of probability distributions on finite sets”, Proc. Mat. Inst. Steklova, 301 (2018), 304–318 | DOI | MR | Zbl

[4] R. L. Shirtladze, “Om a method for constructing a Boolean value with a given probability distribution”, Discrete Analysis, 7 (1966), 71–80 (Russian)

[5] A. D. Yashunsky, “On probability transformations by read-once Boolean formulas”, Proc. XVI Int. School and Seminar “Synthesis and Complexity of Control Systems” (St. Petersburg, Russia, June 26–30, 2006), Mekh.-Mat. Fak. MGU, M., 2006, 150–155 (Russian)

[6] H. Zhou, P. L. Loh, J. Bruck, The synthesis and analysis of stochastic switching circuits, Cornell Univ., Ithaca, NY, 2012, arXiv: 1209.0715

[7] D. Wilhelm, J. Bruck, L. Qian, “Probabilistic switching circuits in DNA”, Proc. Nat. Acad. Sci. USA, 115 (2018), 903–908 | DOI

[8] D. Lee, J. Bruck, “Generating probability distributions using multivalued stochastic relay circuits”, Proc. 2011 IEEE Int. Symp. Information Theory (St. Petersburg, Russia, July 31–Aug. 5, 2011), IEEE, Piscataway, 2011, 308–312 | DOI

[9] D. T. Lee, J. Bruck, “Algorithms for generating probabilities with multivalued stochastic relay circuits”, IEEE Trans. Comput., 64:12 (2015), 3376–3388 | DOI | MR | Zbl