Abstract:
Randomized algorithms of Monte Carlo method are constructed by the combined realization of the base probabilistic model and its random parameters for investigation of the parametric distribution of linear functionals. The optimization of algorithms with the use of the statistical kernel estimator for the probability density is presented. The randomized projection algorithm for estimating a nonlinear functional distribution as applied to the investigation of criticality fluctuations for the particles multiplication process in a random medium is formulated.
Key words:
probabilistic model, statistic modeling, random parameter, randomized algorithm, double randomization method, random medium, splitting method, statistic kernel estimator.
This work was performed within the framework of the State Order for the SB RAS Institute of Computational Mathematics and Mathematical Geophysics (project no. 0315-2016-0002) and was partly supported by the Russian Foundation for Basic Research (project nos. 16-01-00530, 17-01-00823, and 18-01-00356).
Citation:
G. A. Mikhailov, “Randomized algorithms of Monte Carlo method for problems with random parameters (“double randomization” method)”, Sib. Zh. Vychisl. Mat., 22:2 (2019), 187–200; Num. Anal. Appl., 12:2 (2019), 155–165
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\paper Randomized algorithms of Monte Carlo method for problems with random parameters (“double randomization” method)
\jour Sib. Zh. Vychisl. Mat.
\yr 2019
\vol 22
\issue 2
\pages 187--200
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\crossref{https://doi.org/10.15372/SJNM20190205}
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\jour Num. Anal. Appl.
\yr 2019
\vol 12
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\pages 155--165
\crossref{https://doi.org/10.1134/S1995423919020058}
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Linking options:
https://www.mathnet.ru/eng/sjvm709
https://www.mathnet.ru/eng/sjvm/v22/i2/p187
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T. Bulgakova, A. V. Voitishek, “Conditional optimization of the functional computational kernel algorithm for approximating the probability density on the basis of a given sample”, Comput. Math. Math. Phys., 61:9 (2021), 1401–1415
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