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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
Published electronically: August 10, 2016
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Abstract: The reliability and accuracy in the space $ C(T)$ of the Monte Carlo method for evaluating multiple integrals are established.


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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