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General Principles of the Monte Carlo Method

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Monte Carlo Methods

Part of the book series: Monographs on Applied Probability and Statistics ((MSAP))

Abstract

Every Monte Carlo computation that leads to quantitative results may be regarded as estimating the value of a multiple integral. For suppose that no computation requires more than N(= 1010 say) random numbers; then the results will be a (vector-valued) function

$$R\left( {{\xi _1},\xi , \ldots ,{\xi _N}} \right)$$
(5.1.1)

of the sequence of random numbers ξ1,ξ2,…. This is an unbiased estimator of

$$\int_0^1 {...} \int_0^1 {} R\left( {{x_1}....,{x_N}} \right)d{x_1}...d{x_N}.$$
(5.1.2)

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Author information

Authors and Affiliations

  1. Oxford University Institute of Economics and Statistics, UK

    J. M. Hammersley

  2. Oxford University Computing Laboratory, UK

    D. C. Handscomb

Authors
  1. J. M. Hammersley
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  2. D. C. Handscomb
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© 1964 J. M. Hammersley and D. C. Handscomb

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Hammersley, J.M., Handscomb, D.C. (1964). General Principles of the Monte Carlo Method. In: Monte Carlo Methods. Monographs on Applied Probability and Statistics. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5819-7_5

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  • DOI: https://doi.org/10.1007/978-94-009-5819-7_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-5821-0

  • Online ISBN: 978-94-009-5819-7

  • eBook Packages: Springer Book Archive

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