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
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
MathSciNet review:
3553426
Full-text PDF Free Access
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Additional Information
Abstract: The reliability and accuracy in the space $C(T)$ of the Monte Carlo method for evaluating multiple integrals are established.
References
- 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), no. 2, 155–168. MR 2819705, DOI 10.1515/MCMA.2011.007
- Yu. V. Kozachenko and Yu. Yu. Mlavets′, The Banach spaces of $\textbf {F}_\psi (\Omega )$ of random variables, Teor. Ĭmovīr. Mat. Stat. 86 (2011), 92–107 (Ukrainian, with English, Russian and Ukrainian summaries); English transl., Theory Probab. Math. Statist. 86 (2013), 105–121. MR 2986453, DOI 10.1090/S0094-9000-2013-00892-8
- 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)
- 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.
- Yu. Kozachenko and Yu. Mlavets, Stochastic processes of $\mathbf {F}_\psi (\Omega )$ spaces, Contemporary Math. Stat. 2 (2014), no. 1, 55–75.
- 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)
References
- 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
- 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
- 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)
- 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.
- Yu. Kozachenko and Yu. Mlavets, Stochastic processes of $\mathbf {F}_\psi (\Omega )$ spaces, Contemporary Math. Stat. 2 (2014), no. 1, 55–75.
- 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
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
