This article is cited 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.

UDC: 519.676

Received: 21.09.2013

DOI: 10.7868/S004446691309010X

 English version: Computational Mathematics and Mathematical Physics, 2013, 53:9, 1323–1335

Bibliographic databases:

• 
• 
• 
•