Resumen de Convergence of the approximations of an integral by sums of random variables

Vicente Hernández García , Henar Urmeneta Martín-Calero

• Numeric methods of approximation on an integral suggest, in a natural way, random methods of approximation by just evaluating approximation rules in random points.

  In Einmahl-Van Zuijlen (1997) random approximations of the integral of a smooth function on [0,1], based on the trapezoidal rule and Simpson¿s rule, are proposed. They obtain results for the convergence in probability, in the first case, and for the convergence in distribution, in the second case. The purpose of the present paper is to prove similar results for the almost sure convergence. We obtain the rate of almost sure convergence when smooth-conditions on f are holden