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I. N. Medvedev, G. A. Mikhailov

Optimization of Monte Carlo weighted methods for part of variables

We consider problems whose mathematical model is associated with a certain Markov chain, in this case it is necessary to estimate the linear functionals of the solution to the corresponding integral equation of the second kind. Auxiliary variables whose values define transitions in the initial chain are included in the number of coordinates of the phase space to construct the weight modifications of numerical statistical simulation. Auxiliary weight after the realization of each auxiliary random variable is multiplied by the ratio of the corresponding densities of the initial distribution to the modelled one. In this paper, we solve the minimization problem of the variances of the estimates for linear functionals by varying the modelled distribution density of one (the first in order) auxiliary, maybe vector, random variable.

Russian Journal of Numerical Analysis and Mathematical Modelling, Walter de Gruyter

Print ISSN: 0927-6467
Volume: 18, 10/2003
Pages: 413 - 428

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