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Randomized Monte Carlo Algorithms for Problems with Random Parameters (“Double Randomization” Method)

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Abstract

Randomized Monte Carlo algorithms are constructed by a combination of a basic probabilistic model and its random parameters to investigate parametric distributions of linear functionals. An optimization of the algorithms with a statistical kernel estimator for the probability density is presented. A randomized projection algorithm for estimating a nonlinear functional distribution is formulated and applied to the investigation of the criticality fluctuations of a particle multiplication process in a random medium.

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Acknowledgements

The author would like to thank his former PhD students G.Z. Lotova, A.Yu. Ambos, and others for active participation in the development and realization of randomized algorithms for the Monte Carlo method.

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Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090, Russia

    G. A. Mikhailov

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    G. A. Mikhailov

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  1. G. A. Mikhailov
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Correspondence to G. A. Mikhailov.

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Russian Text © The Author(s), 2019, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2019, Vol. 22, No. 2, pp. 187–200.

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Mikhailov, G.A. Randomized Monte Carlo Algorithms for Problems with Random Parameters (“Double Randomization” Method). Numer. Analys. Appl. 12, 155–165 (2019). https://doi.org/10.1134/S1995423919020058

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  • DOI: https://doi.org/10.1134/S1995423919020058

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