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Variance reduction in Monte Carlo methods and optimization problems in \({\mathbb{R}}^ n\). (Italian. English summary) Zbl 0601.65003
In the framework of Monte Carlo methods a technique for reducing the variance is considered. Generalizing a procedure suggested by the second author, Probabilistic estimation of error in Richardson extrapolation. ibid. 20, 455-465 (Italian) (1983), we give a method which reduces the variance by solving an unconstrained optimization problem. Concerned with the approximate integration, some numerical tests are considered. The described technique is shown to allow more accurate results than some known ones.
MSC:
65C05 Monte Carlo methods
65D32 Numerical quadrature and cubature formulas
65K10 Numerical optimization and variational techniques
62F10 Point estimation
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