Random Designs for Estimating Integrals of Stochastic Processes
估计随机过程积分的随机采样设计
The integral of a second-order stochastic process $Z$ over a $d$-dimensional domain is estimated by a weighted linear combination of observations of $Z$ in a random design. The design sample points are possibly dependent random variables and are independent of the process $Z$, which may be nonstationary. Necessary and sufficient conditions are obtained for the mean squared error of a random design estimator to converge to zero as the sample size increases towards infinity.…