Improvement of Multidimensional Randomized Monte Carlo Algorithms with “Splitting”

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Abstract: Randomized Monte Carlo algorithms are constructed by jointly realizing a baseline probabilistic model of the problem and its random parameters (random medium) in order to study a parametric distribution of linear functionals. This work relies on statistical kernel estimation of the multidimensional distribution density with a “homogeneous” kernel and on a splitting method, according to which a certain number n of baseline trajectories are modeled for each medium realization. The optimal value of n is estimated using a criterion for computational complexity formulated in this work. Analytical estimates of the corresponding computational efficiency are obtained with the help of rather complicated calculations.

Original languageEnglish
Pages (from-to)775-781
Number of pages7
JournalComputational Mathematics and Mathematical Physics
Issue number5
Publication statusPublished - 1 May 2019


  • complexity of functional estimate
  • double randomization method
  • Monte Carlo method
  • probabilistic model
  • random medium
  • randomized algorithm
  • splitting method
  • statistical kernel estimate
  • statistical modeling

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