This article is cited in 8 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.

UDC: 519.676

Received: 22.07.2009

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

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