INTERPOLATION, QUADRATURE, AND STOCHASTIC INTEGRATION
统一了数值积分与随机积分方法，提出用插值函数作为控制变量来缩减模拟方差，并通过高斯求积的数值案例展示效果。
This paper considers features in numerical and stochastic integration approaches for the evaluation of analytically intractable integrals. It provides a unification of these two approaches. Some important features in quadrature 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 in simulation. We illustrate possible variance reduction by some numerical cases with Gaussian quadrature. The resulting simulator may also be regarded as a monitor of the approximation error of a quadrature.