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Theory of Probability and Mathematical Statistics

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An application of the theory of spaces $ \mathbf{F}_\psi(\Omega)$ for evaluating multiple integrals by using the Monte Carlo method


Authors: Yu. V. Kozachenko and Yu. Yu. Mlavets
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 92 (2015).
Journal: Theor. Probability and Math. Statist. 92 (2016), 59-69
MSC (2010): Primary 60G07; Secondary 65C05
DOI: https://doi.org/10.1090/tpms/982
Published electronically: August 10, 2016
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Abstract | References | Similar Articles | Additional Information

Abstract: The reliability and accuracy in the space $ C(T)$ of the Monte Carlo method for evaluating multiple integrals are established.


References [Enhancements On Off] (What's this?)

  • 1. Yu. V. Kozachenko and Yu. Yu. Mlavets, Probability of large deviations of sums of random processes from Orlicz space, Monte Carlo Methods Appl. 17 (2011), 155-168. MR 2819705
  • 2. Yu. V. Kozachenko and Yu. Yu. Mlavets, The Banach space $ \mathbf {F}_\psi (\Omega )$ of random variables, Teor. Ĭmovir. Mat. Stat. 86 (2012), 92-107; English transl. in Theor. Probability and Math. Statist. 86 (2013), 105-121. MR 2986453
  • 3. S. V. Ermakov and E. I. Ostrovskiĭ, Conditions for the continuity, exponential bounds, and central limit theorem for random fields, Dep. VINITI no. 3752-B.86.0, 1986. (Russian)
  • 4. Yu. Yu. Mlavets, $ \mathbf {F}_\psi (\Omega )$-spaces of random variables with exponential function $ \psi $, Visnyk Kyiv Taras Shevchenko National University Phys. Math. 2 (2012), 19-22.
  • 5. Yu. Kozachenko and Yu. Mlavets, Stochastic processes of $ \mathbf {F}_\psi (\Omega )$ spaces, Contemporary Math. Stat. 2 (2014), no. 1, 55-75.
  • 6. Yu. Yu. Mlavets, Conditions for the uniform convergence of random series of functions belonging to the spaces $ \mathbf {F}_\psi (\Omega )$, Appl. Stat. Actuar. Finance Math. 1 (2014), 97-103. (Ukrainian)

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Additional Information

Yu. V. Kozachenko
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email: ykoz@ukr.net

Yu. Yu. Mlavets
Affiliation: Department of Cybernetics and Applied Mathematics, Faculty for Mathematics, Uzhgorod National University, Universytets’ka Street, 14, Uzhgorod 88000, Ukraine
Email: yura-mlavec@ukr.net

DOI: https://doi.org/10.1090/tpms/982
Keywords: Spaces $\mathbf{F}_\psi(\Omega)$ of random variables, majorant characteristic, stochastic processes, Monte Carlo method
Received by editor(s): February 15, 2015
Published electronically: August 10, 2016
Article copyright: © Copyright 2016 American Mathematical Society

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