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

Author

Listed:
  • 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)

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} .

Suggested Citation

  • Bryzgalov Viktor & Shlimbetov Nurlibay & Voytishek Anton, 2024. "Choice of a constant in the expression for the error of the Monte Carlo method," Monte Carlo Methods and Applications, De Gruyter, vol. 30(2), pages 131-136.
    • Handle: RePEc:bpj:mcmeap:v:30:y:2024:i:2:p:131-136:n:1007
    DOI: 10.1515/mcma-2024-2004
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