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Monte Carlo Methods

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Book cover Randomized Algorithms for Analysis and Control of Uncertain Systems

Part of the book series: Communications and Control Engineering ((CCE))

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Abstract

This chapter studies Monte Carlo and quasi-Monte Carlo methods for integration, optimization, and probability and expected value estimation. The Monte Carlo method has been widely used for simulations of various physical and mathematical systems and has a very long history that began in 1949 with the seminal paper of Metropolis and Ulam. The name Monte Carlo probably originated from the famous casino in Monaco and reflects the random and repetitive nature of the process, which is similar to gambling in casinos. The quasi-Monte Carlo method is more recent and may be regarded as a deterministic version of Monte Carlo.

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Notes

  1. 1.

    The semi-open unit cube is defined as [0,1)n≐{x∈ℝn:x i ∈[0,1), i=1,…,n}.

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Authors and Affiliations

  1. CNR - IEIIT, Politecnico di Torino, Turin, Italy

    Roberto Tempo & Fabrizio Dabbene

  2. Dip. Automatica e Informatica, Politecnico di Torino, Turin, Italy

    Giuseppe Calafiore

Authors
  1. Roberto Tempo
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  2. Giuseppe Calafiore
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  3. Fabrizio Dabbene
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© 2013 Springer-Verlag London

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Tempo, R., Calafiore, G., Dabbene, F. (2013). Monte Carlo Methods. In: Randomized Algorithms for Analysis and Control of Uncertain Systems. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-4610-0_7

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  • DOI: https://doi.org/10.1007/978-1-4471-4610-0_7

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-4609-4

  • Online ISBN: 978-1-4471-4610-0

  • eBook Packages: EngineeringEngineering (R0)

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