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A New Criterion for Finiteness of Weight Estimator Variance in Statistical Simulation

In: Monte Carlo and Quasi-Monte Carlo Methods 2006

Author

Listed:
  • Ilya Medvedev

    (Institute of Computational Mathematics and Mathematical Geophysics)

  • Gennadii Mikhailov

    (Institute of Computational Mathematics and Mathematical Geophysics)

Abstract

Summary It has been found recently that an increase in phase space dimension by including simulated auxiliary random variables in the number of phase coordinates can be effective for the construction of weight modifications. In this paper the effectiveness of “value” and partial “value” modelling is considered. These types of modelling are related to the construction of simulated distribution for some auxiliary random variable by multiplying the initial density by the “value” function which is usually corresponds to the solution of adjoint integral equation of the second kind. It is proved that the weight estimator variance in case of the partial value modelling is finite. On the basis of this fact a new criterion based on the use of majorant adjoint equation was proposed for finiteness of the weight estimator variance. Using this criterion the classical “exponential transformation” method is studied for the free path simulation in one and three dimensional modifications.

Suggested Citation

  • Ilya Medvedev & Gennadii Mikhailov, 2008. "A New Criterion for Finiteness of Weight Estimator Variance in Statistical Simulation," Springer Books, in: Alexander Keller & Stefan Heinrich & Harald Niederreiter (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2006, pages 561-576, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-74496-2_33
    DOI: 10.1007/978-3-540-74496-2_33
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