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Theory of Probability and Mathematical Statistics



An application of the theory of spaces Fψ(Ω) for evaluating multiple integrals by using the Monte Carlo method

Yu. V. Kozachenko, Yu. Yu. Mlavets

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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.

Keywords: Spaces Fψ(Ω) of random variables, majorant characteristic, stochastic processes, Monte Carlo method

Bibliography:
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.
2. Yu. V. Kozachenko and Yu. Yu. Mlavets, The Banach space Fψ(Ω) of random variables, Teor. Ĭmovir. Mat. Stat. 86 (2012), 92-107; English transl. in Theor. Probability and Math. Statist. 86 (2013), 105-121.
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, Fψ(Ω)-spaces of random variables with exponential function ψ, Visnyk Kyiv Taras Shevchenko National University Phys. Math. 2 (2012), 19-22.
5. Yu. Kozachenko and Yu. Mlavets, Stochastic processes of Fψ(Ω) 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 Fψ(Ω), Appl. Stat. Actuar. Finance Math. 1 (2014), 97-103. (Ukrainian)