On the number of random digits required in montecarlo integration of definable functions

Authors:
César L. Alonso;Josè L. Montaña;Luis M. Pardo
Affiliations:
Centro de Inteligencia Artificial, Universidad de Oviedo, Gijón, Spain;Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, Spain;Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, Spain
Venue:
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Year:
2005

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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.