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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 2, Pages 362–374 (Mi zvmmf4835)  

This article is cited in 6 scientific papers (total in 6 papers)

Estimation of the criticality parameters of branching processes by the Monte Carlo method

S. A. Brednikhin, I. N. Medvedev, G. A. Mikhaĭlov

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

Abstract: Monte Carlo algorithms designed for the estimation of the criticality parameters of multiplying particle transport processes (actually, these are inhomogeneous branching processes) are described and examined. The effective multiplication factor and the time multiplication constant are used as the basic criticality parameters. Algorithms for the direct simulation of “trees” of trajectories are considered as algorithms for the statistical modeling of the iterations of an integral operator with the kernel equal to the substochastic density of the transition to the next generation of fission events in the corresponding phase space. These algorithms provide a basis for constructing effective statistical estimates of the criticality parameters (with regard to the sequence of generations with different indexes) and for the analysis of the corresponding error.

Key words: branching stochastic process, effective multiplication factor, time multiplication constant, variance of the weight estimate, differential entropy, Shannon entropy, Monte Carlo method.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:2, 345–356

Bibliographic databases:

UDC: 519.676
Received: 22.07.2009

Citation: S. A. Brednikhin, I. N. Medvedev, G. A. Mikhaǐlov, “Estimation of the criticality parameters of branching processes by the Monte Carlo method”, Zh. Vychisl. Mat. Mat. Fiz., 50:2 (2010), 362–374; Comput. Math. Math. Phys., 50:2 (2010), 345–356

Citation in format AMSBIB
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    2. Prokhorov I.V., Zhuplev A.S., “Ob effektivnosti metodov maksimalnogo secheniya v teorii perenosa izlucheniya”, Kompyuternye issledovaniya i modelirovanie, 5:4 (2013), 573–582  elib
    3. G. A. Mikhailov, “About efficient algorithms of numerically-statistical simulation”, Num. Anal. Appl., 7:2 (2014), 147–158  mathnet  crossref  mathscinet
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    5. Ambos A.Yu., Lotova G., Mikhailov G., “New Monte Carlo Algorithms For Investigation of Criticality Fluctuations in the Particle Scattering Process With Multiplication in Stochastic Media”, Russ. J. Numer. Anal. Math. Model, 32:3 (2017), 165–172  crossref  mathscinet  zmath  isi  scopus
    6. G. A. Mikhailov, G. Z. Lotova, “Monte Carlo methods for estimating the probability distributions of criticality parameters of particle transport in a randomly perturbed medium”, Comput. Math. Math. Phys., 58:11 (2018), 1828–1837  mathnet  crossref  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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