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On the Number of Random Digits Required in MonteCarlo Integration of Definable Functions
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Papers
On the Number of Random Digits Required in MonteCarlo Integration of Definable Functions César L. Alonso1  , Josè L. Montaña2 and Luis M. Pardo2
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Centro de Inteligencia Artificial, Universidad de Oviedo, Campus de Viesques, 33271 Gijón, Spain |
| (2) |
Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, Spain |
Abstract
Semi-algebraic objects are subsets or functions that can be described by finite boolean combinations of polynomials with real coefficients. In this paper we provide sharp estimates for the the precision and the number of trials needed in the MonteCarlo integration method to achieve a given error with a fixed confidence when approximating the mean value of semi-algebraic functions. Our study extends to the functional case the results of P. Koiran ([7]) for approximating the volume of semi-algebraic sets.
Keywords: MonteCarlo algorithms, discrepancy bounds, learning theory, Chebyshev inequalities, semi-algebraic geometry.
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