Choice of a constant in the expression for the error of the Monte Carlo method

Bryzgalov Viktor (), Shlimbetov Nurlibay () and Voytishek Anton ()
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Bryzgalov Viktor: Lyceum No. 130, Novosibirsk, Russia
Shlimbetov Nurlibay: Novosibirsk State University, Novosibirsk, Russia
Voytishek Anton: Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Novosibirsk State University, Novosibirsk, Russia

Monte Carlo Methods and Applications, 2024, vol. 30, issue 2, 131-136

Abstract: This paper considers three approaches to choosing the constant H in the expression H ⁢ 𝐃 ⁢ ζ / n {H\sqrt{{\mathbf{D}}\zeta}/\sqrt{n}} for the error of the Monte Carlo method for numerical calculation of mathematical expectation 𝐄 ⁢ ζ {{\mathbf{E}}\zeta} of a random variable ζ: in probability, in mean square and in mean.In practical studies using the Monte Carlo method, when estimating the calculation error, it is recommended to use the “in mean” approach with the constant H = 2 π = 0.79788456079 ⁢ … {H=\sqrt{\frac{2}{\pi}}=0.79788456079\dots} .

Keywords: General scheme of the Monte Carlo method; computer approximation of mathematical expectation using sample mean; error of the Monte Carlo method; choice of a constant in the expression for the error of the Monte Carlo method (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1515/mcma-2024-2004

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