This article is cited in 1 paper

Modification of two-step Monte Carlo algorithms based on the symmetry of the first step

G. A. Mikhailov^a, S. A. Rozhenko<sup>b

a</sup> Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Lavrent'eva 6, Novosibirsk, 630090, Russia
^b Novosibirsk State University, Universitetskii pr. 2, Novosibirsk, 630090, Russia

Abstract: Two-step Monte Carlo algorithms are modified taking into account the symmetry (i.e., invariance) of the first step about some initial vector parameter of the modeled trajectory. In the modification, the modeling of this parameter is formally transferred to the second step of the algorithm. In the “splitting method”, this means the randomization of the initial points of auxiliary trajectories. It is shown that the randomization can be improved by applying the Bellman principle.

Key words: Monte Carlo method, two-step algorithm, splitting method, complexity estimation for algorithms.

UDC: 519.676

Received: 04.05.2009

 English version: Computational Mathematics and Mathematical Physics, 2009, 49:11, 1921–1929

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