Randomized algorithms of Monte Carlo method for problems with random parameters (“double randomization” method)
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 22 (2019) no. 2, pp. 187-200.

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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.
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     title = {Randomized algorithms of {Monte} {Carlo} method for problems with random parameters ({\textquotedblleft}double randomization{\textquotedblright} method)},
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G. A. Mikhailov. Randomized algorithms of Monte Carlo method for problems with random parameters (“double randomization” method). Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 22 (2019) no. 2, pp. 187-200. http://geodesic.mathdoc.fr/item/SJVM_2019_22_2_a5/

[1] Mikhailov G.A., Optimization of Weighted Monte Carlo Methods, Springer-Verlag, 1992 | MR | MR

[2] Ambos A.Yu., Mikhailov G.A., “Effective averaging of stochastic radiative models based on Monte Carlo simulation”, Comput. Maths. and Math. Phys., 56:5 (2016), 881-893 | DOI | DOI | MR | Zbl

[3] Mikhaylov G.A., “Effektivnye algoritmy metoda Monte-Karlo dlya vychisleniya korrelyatsionnyh harakteristik uslovnyh matematicheskih ozhidaniy”, Zhurn. vychisl. matem. i mat. fiziki, 17:1 (1977), 246-249 | MR

[4] Mikhaylov G.A., Voytishek A.V., Chislennoe statisticheskoe modelirovanie. Metody Monte-Karlo, Uchebnoe posobie, Izd. tsentr “Akademiya”, M., 2006

[5] Marchuk G.I., Mikhailov G.A., Nazaraliev M.A., Darbinjan R.A., Kargin B.A., Elepov B.S., The Monte Carlo Methods in Atmospheric Optics, Springer, Berlin–Heidelberg, 1980 | MR | MR

[6] Ambos A.Yu., “Numerical Models of Mosaic Homogeneous Isotropic Random Fields and Problems of Radiative Transfer”, Numerical Analysis and Applications, 9:1 (2016), 12-23 | DOI | MR | Zbl

[7] Parsen E., “On estimation of a probability density function and mode”, Ann. Math. Statist., 1962, no. 35, 1065-1076 | DOI | MR

[8] Borovkov A.A., Matematicheskaya statistika, Izd-vo IM SO RAN, Novosibirsk, 1997 | MR

[9] Mikhailov G.A., Prigarin S.M., Rozhenko S.A., “Comparative analysis of vector algorithms for statistical modelling of radiative transfer process”, Russ. J. Num. Anal. Math. Model., 33:4 (2018), 220-229 | MR

[10] Lotova G.Z. Monte Carlo algorithms for calculation of diffusive characteristics of an electron avalanche in gases, Russ. J. Num. Anal. Math. Model., 31:6 (2011), 369-377 | MR

[11] Epanechnikov V.A., “Non-parametric estimation of a multivariate probability density”, Theory Probab. Appl., 14:1 (1969), 153-158 | DOI | MR

[12] Chentsov N.N., Statisticheskie reshayushchie pravila i optimal'nye vyvody, Nauka, M., 1972

[13] Mikhailov G.A., Tracheva N.V., Ukhinov S.A., “Randomized projection method for estimating angular distributions of polarized radiation based on numerical statistical modeling”, Comput. Maths. and Math. Phys., 56:9 (2016), 1540-1550 | DOI | DOI | MR | Zbl

[14] Mikhailov G.A., Lotova G.Z., “Monte Carlo methods for estimating the probability distributions of criticality parameters of particle transport in a randomly pertubated medium”, Comput. Maths. and Math. Phys., 58:11 (2018), 1828-1837 | DOI | DOI | MR | Zbl

[15] Vladimirov V.S., “O primenenii metoda Monte-Karlo dlya otyskaniya naimen'shego harakteristicheskogo chisla i sootvetstvuyushchey sobstvennoy funktsii lineynogo integral'nogo uravneniya”, Teoriya veroyatnostey i ee primenenie, 1:1 (1956), 113-130 | Zbl

[16] Ermakov S.M., Mikhaylov G.A., Statisticheskoe modelirovanie, Nauka, M., 1982 | MR

[17] Ambos A.Yu., Mikhailov G.A., “Monte Carlo Estimation of Functional Characteristics of Field Intensity of Radiation Passing through a Random Medium”, Numerical Analysis and Applications, 11:4 (2018), 279-292 | DOI | MR

[18] Woodcock E., Murphy T., Hemmings P., Longworth S., “Techniques used in the GEM code for Monte Carlo neutronics calculations in reactors and other systems of complex geometry”, Proc. Conf. Applications of Computing Methods to Reactor Problems, 1965, 557-557

[19] Averina T.A., Mikhailov G.A., “Algorithms for exact and approximate statistical simulation of Poisson ensembles”, Comput. Maths. and Math. Phys., 50:6 (2010), 951-962 | DOI | MR | Zbl

[20] Belyaev Yu.K., Veroyatnost' i matematicheskaya statistika. Entsiklopediya, Nauchn. izd-vo BPE, M., 1999