Standard

Improvement of Multidimensional Randomized Monte Carlo Algorithms with “Splitting”. / Mikhailov, G. A.

In: Computational Mathematics and Mathematical Physics, Vol. 59, No. 5, 01.05.2019, p. 775-781.

Research output: Contribution to journal › Article › peer-review

Harvard

Mikhailov, GA 2019, 'Improvement of Multidimensional Randomized Monte Carlo Algorithms with “Splitting”', Computational Mathematics and Mathematical Physics, vol. 59, no. 5, pp. 775-781. https://doi.org/10.1134/S0965542519050117

APA

Mikhailov, G. A. (2019). Improvement of Multidimensional Randomized Monte Carlo Algorithms with “Splitting”. Computational Mathematics and Mathematical Physics, 59(5), 775-781. https://doi.org/10.1134/S0965542519050117

Vancouver

Mikhailov GA. Improvement of Multidimensional Randomized Monte Carlo Algorithms with “Splitting”. Computational Mathematics and Mathematical Physics. 2019 May 1;59(5):775-781. doi: 10.1134/S0965542519050117

Author

Mikhailov, G. A. / Improvement of Multidimensional Randomized Monte Carlo Algorithms with “Splitting”. In: Computational Mathematics and Mathematical Physics. 2019 ; Vol. 59, No. 5. pp. 775-781.

BibTeX

@article{9e4678a3b9a6490aac3748f71aace0c9,
title = "Improvement of Multidimensional Randomized Monte Carlo Algorithms with “Splitting”",
abstract = "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.",
keywords = "complexity of functional estimate, double randomization method, Monte Carlo method, probabilistic model, random medium, randomized algorithm, splitting method, statistical kernel estimate, statistical modeling, MODELS",
author = "Mikhailov, {G. A.}",
year = "2019",
month = may,
day = "1",
doi = "10.1134/S0965542519050117",
language = "English",
volume = "59",
pages = "775--781",
journal = "Computational Mathematics and Mathematical Physics",
issn = "0965-5425",
publisher = "PLEIADES PUBLISHING INC",
number = "5",

}

RIS

TY - JOUR

T1 - Improvement of Multidimensional Randomized Monte Carlo Algorithms with “Splitting”

AU - Mikhailov, G. A.

PY - 2019/5/1

Y1 - 2019/5/1

N2 - 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.

AB - 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.

KW - complexity of functional estimate

KW - double randomization method

KW - Monte Carlo method

KW - probabilistic model

KW - random medium

KW - randomized algorithm

KW - splitting method

KW - statistical kernel estimate

KW - statistical modeling

KW - MODELS

UR - http://www.scopus.com/inward/record.url?scp=85067460114&partnerID=8YFLogxK

U2 - 10.1134/S0965542519050117

DO - 10.1134/S0965542519050117

M3 - Article

AN - SCOPUS:85067460114

VL - 59

SP - 775

EP - 781

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 5

ER -

ID: 20643071