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Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 9, Pages 1503–1516 (Mi zvmmf9917)  

This article is cited in 3 scientific papers (total in 3 papers)

Parametric weighted minimax estimates in Monte-Carlo methods

G. A. Mikhailov, S. A. Rozhenko

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

Abstract: In the similar trajectory method (STM), the numerical-statistical modeling of trajectories of particles (radiation quanta) is implemented by applying an auxiliary radiation model. Weighted estimates of the functionals are calculated simultaneously for a set physical parameters values. Theoretical and numerical aspects of choosing an auxiliary model with the aim of minimizing the parametric maximum of the mean-square error in weighted estimates are discussed. Previously known results concerning minimax STM algorithms are refined, and new assertions are obtained. The STM is used to numerically study the parametric dependence of the “transport approximation” error for the particle transmission, absorption, and reflection probabilities.

Key words: Monte-Carlo method, similar trajectory method, minimax algorithms.

DOI: https://doi.org/10.7868/S004446691309010X

Full text: PDF file (489 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:9, 1323–1335

Bibliographic databases:

UDC: 519.676
Received: 21.09.2013

Citation: G. A. Mikhailov, S. A. Rozhenko, “Parametric weighted minimax estimates in Monte-Carlo methods”, Zh. Vychisl. Mat. Mat. Fiz., 53:9 (2013), 1503–1516; Comput. Math. Math. Phys., 53:9 (2013), 1323–1335

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Mikhailov G.A., “New Results and Problems in the Theory of Algorithms of Statistical Simulation of Radiation Transfer”, Russ. J. Numer. Anal. Math. Model, 30:2 (2015), 103–109  crossref  mathscinet  zmath  isi  elib  scopus
    2. Medvedev I.N., “The method of similar trajectories with branching according to parametric maximum of the auxiliary weight”, Russ. J. Numer. Anal. Math. Model, 31:6 (2016), 379–385  crossref  mathscinet  zmath  isi  scopus
    3. Mikhailov G.A. Prigarin S.M. Rozhenko S.A., “Weighted Monte Carlo estimators for angular distributions of the solar radiation reflected from a cloud layer”, Russ. J. Numer. Anal. Math. Model, 31:4 (2016), 197–205  crossref  mathscinet  zmath  isi  elib  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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