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

IF 0.8 Q3 STATISTICS & PROBABILITY Monte Carlo Methods and Applications Pub Date : 2024-04-24 DOI:10.1515/mcma-2024-2004

Viktor Bryzgalov, Nurlibay Shlimbetov, Anton Voytishek

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引用次数: 0

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}

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蒙特卡罗方法误差表达式中常数的选择

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} .

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来源期刊

Monte Carlo Methods and Applications STATISTICS & PROBABILITY-

CiteScore

1.20

自引率

22.20%

发文量