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Monte Carlo Methods and Applications

Managing Editor: Sabelfeld, Karl K.

Editorial Board: Binder, Kurt / Bouleau, Nicolas / Chorin, Alexandre J. / Dimov, Ivan / Dubus, Alain / Egorov, Alexander D. / Ermakov, Sergei M. / Halton, John H. / Heinrich, Stefan / Kalos, Malvin H. / Lepingle, D. / Makarov, Roman / Mascagni, Michael / Mathe, Peter / Niederreiter, Harald / Platen, Eckhard / Sawford, Brian R. / Schmid, Wolfgang Ch. / Schoenmakers, John / Simonov, Nikolai A. / Sobol, Ilya M. / Spanier, Jerry / Talay, Denis

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Volume 21, Issue 3


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

Yuriy V. Kozachenko
  • 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
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/ Yuriy Y. Mlavets
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  • Department of Cybernetics and Applied Mathematics, Faculty of Mathematics, Uzhhorod National University, University Str. 14, Uzghorod 88000, Ukraine
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Published Online: 2015-09-01 | DOI: https://doi.org/10.1515/mcma-2015-0104


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.

Keywords: 𝐅ψ(Ω) space of random variables; condition 𝐇; Monte Carlo method; random process

MSC: 65C05; 60G07

About the article

Received: 2015-03-02

Accepted: 2015-08-12

Published Online: 2015-09-01

Published in Print: 2015-09-01

Citation Information: Monte Carlo Methods and Applications, Volume 21, Issue 3, Pages 233–244, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: https://doi.org/10.1515/mcma-2015-0104.

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