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Reliability and accuracy in the space Lp(T) for the calculation of integrals depending on a parameter by the Monte Carlo method

Author

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  • Kozachenko Yuriy V.

    (Department of Probability Theory, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska Str. 64, Kyiv 01601, Ukraine)

  • Mlavets Yuriy Y.

    (Department of Cybernetics and Applied Mathematics, Faculty of Mathematics, Uzhhorod National University, University Str. 14, Uzghorod 88000, Ukraine)

Abstract

This paper is devoted to the estimation of the accuracy and reliability (in Lp(T) metrics) for the calculation of improper integrals depending on a parameter t using the Monte Carlo method. For this estimates we use the theory of 𝐅ψ(Ω) spaces.

Suggested Citation

  • Kozachenko Yuriy V. & Mlavets Yuriy Y., 2015. "Reliability and accuracy in the space Lp(T) for the calculation of integrals depending on a parameter by the Monte Carlo method," Monte Carlo Methods and Applications, De Gruyter, vol. 21(3), pages 233-244, September.
    • Handle: RePEc:bpj:mcmeap:v:21:y:2015:i:3:p:233-244:n:4
    DOI: 10.1515/mcma-2015-0104
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    References listed on IDEAS

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    1. Kurbanmuradov O. & Sabelfeld K., 2006. "Exponential bounds for the probability deviations of sums of random fields," Monte Carlo Methods and Applications, De Gruyter, vol. 12(3), pages 211-229, October.
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    1. Kozachenko Yu. V. & Mlavets Yu. Yu., 2011. "Probability of large deviations of sums of random processes from Orlicz space," Monte Carlo Methods and Applications, De Gruyter, vol. 17(2), pages 155-168, January.

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