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Improvement of Multidimensional Randomized Monte Carlo Algorithms with “Splitting”

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Abstract

Randomized Monte Carlo algorithms are constructed by jointly realizing a baseline probabilistic model of the problem and its random parameters (random medium) in order to study a parametric distribution of linear functionals. This work relies on statistical kernel estimation of the multidimensional distribution density with a “homogeneous” kernel and on a splitting method, according to which a certain number \(n\) of baseline trajectories are modeled for each medium realization. The optimal value of \(n\) is estimated using a criterion for computational complexity formulated in this work. Analytical estimates of the corresponding computational efficiency are obtained with the help of rather complicated calculations.

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FUNDING

This work was performed within the framework of a state task at the Institute of Computational Mathematics and Mathematical Geophysics of the Siberian Branch of the Russian Academy of Science (project no. 0315-2016-0002) and was supported in part by the Russian Foundation for Basic Research (project nos. 16-01-00530, 17-01-00823, 18-01-00356).

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Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    G. A. Mikhailov

  2. Novosibirsk State University, 630090, Novosibirsk, 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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Translated by I. Ruzanova

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Mikhailov, G.A. Improvement of Multidimensional Randomized Monte Carlo Algorithms with “Splitting”. Comput. Math. and Math. Phys. 59, 775–781 (2019). https://doi.org/10.1134/S0965542519050117

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  • DOI: https://doi.org/10.1134/S0965542519050117

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