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Variance reduction techniques for estimation of integrals over a set of branching trajectories

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Abstract

Monte Carlo variance reduction techniques within the supertrack approach are justified as applied to estimating non-Boltzmann tallies equal to the mean of a random variable defined on the set of all branching trajectories. For this purpose, a probability space is constructed on the set of all branching trajectories, and the unbiasedness of this method is proved by averaging over all trajectories. Variance reduction techniques, such as importance sampling, splitting, and Russian roulette, are discussed. A method is described for extending available codes based on the von Neumann-Ulam scheme in order to cover the supertrack approach.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia

    E. A. Tsvetkov

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  1. E. A. Tsvetkov
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Correspondence to E. A. Tsvetkov.

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Original Russian Text © E.A. Tsvetkov, 2014, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2014, Vol. 54, No. 2, pp. 183–194.

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Tsvetkov, E.A. Variance reduction techniques for estimation of integrals over a set of branching trajectories. Comput. Math. and Math. Phys. 54, 195–205 (2014). https://doi.org/10.1134/S0965542514020122

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