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On the Approximation of Random Variables on a Finite Chain

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Abstract

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.

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REFERENCES

  1. F. I. Salimov, “Finite Generability of Distribution Algebras,” Diskret. Anal. Issled. Oper. Ser. 1, 4 (2), 43–50 (1997).

    MathSciNet  Google Scholar 

  2. R. M. Kolpakov, “Closed Classes of Finite Distributions of Rational Probabilities,” Diskret. Anal. Issled. Oper. Ser. 1, 11 (3), 16–31 (2004).

    MathSciNet  Google Scholar 

  3. A. D. Yashunsky, “Algebras of Probability Distributions on Finite Sets,” Trudy Mat. Inst. Steklov. 301, 320–335 (2018) [Proc. Steklov Inst. Math. 301, 304–318 (2018)].

    Article  MathSciNet  Google Scholar 

  4. R. L. Skhirtladze, “On a Method for Constructing a Boolean Value with a Given Probability Distribution,” in Discrete Analysis, Vol. 7 (Nauka, Novosibirsk, 1966), pp. 71–80.

  5. A. D. Yashunsky, “On Probability Transformations by Read-Once Boolean Formulas,” in Proceedings. XVI International School and Seminar “Synthesis and Complexity of Control Systems” (St. Petersburg, Russia, June 26–30, 2006) (Mekh.-Mat. Fak. MGU, Moscow, 2006), pp. 150–155.

  6. H. Zhou, P.-L. Loh, and J. Bruck, “The Synthesis and Analysis of Stochastic Switching Circuits,” Cornell Univ. Libr. e-Print Archive, arXiv:1209.0715 (Cornell Univ., Ithaca, NY, 2012).

  7. D. Wilhelm, J. Bruck, and L. Qian, “Probabilistic Switching Circuits in DNA,” Proc. Nat. Acad. Sci. U.S.A. 115, 903–908 (2018).

    Article  Google Scholar 

  8. D. Lee and J. Bruck, “Generating Probability Distributions Using Multivalued Stochastic Relay Circuits,” in Proceedings of 2011 IEEE International Symposium on Information Theory (St. Petersburg, Russia, July 31–August 5, 2011) (IEEE, Piscataway, 2011), pp. 308–312.

  9. D. T. Lee and J. Bruck, “Algorithms for Generating Probabilities with Multivalued Stochastic Relay Circuits,” IEEE Trans. Comput. 64 (12), 3376–3388 (2015).

    Article  MathSciNet  Google Scholar 

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ACKNOWLEDGMENTS

The author is grateful to O. M. Kasim-Zade for his attention to this study.

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Moscow, 125047, Russia

    A. D. Yashunsky

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  1. A. D. Yashunsky
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Correspondence to A. D. Yashunsky.

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Translated by Ya.A. Kopylov

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Cite this article

Yashunsky, A.D. On the Approximation of Random Variables on a Finite Chain. J. Appl. Ind. Math. 14, 581–591 (2020). https://doi.org/10.1134/S1990478920030163

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  • DOI: https://doi.org/10.1134/S1990478920030163

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