Interpolation, quadrature, and stochastic integration

This paper considers features in numerical and stochastic integration appro aches for the evaluation of analytically intractable integrals. It provides a unification of these two approaches. Some important features in quadratu re formulations, namely, interpolation and region partition, can provide a valuable device for the design of a stochastic simulator. An interpolating function can be used as a valuable control variate for variance reduction i n simulation. We illustrate possible variance reduction by some numerical c ases with Gaussian quadrature. The resulting simulator may also be regarded as a monitor of the approximation error of a quadrature. The resulting sim ulator may also be regarded as a monitor of the approximation error of a qu adrature.