Random uniform approximation under weighted importance sampling of a class of stratified input

Abstract

We consider random discrepancy under weighted importance sampling of a class of stratified input. We give the expected $L_p-$discrepancy($2\le p<\infty$) upper bound in weighted form under a class of stratified sampling. This result contributes to the error estimate of the upper bound of the integral approximation under weighted importance sampling, and and our sampling pattern is a stratified input.

The author of this article is entirely written by Xiaoda Xu, and Jun Xian did not participate in the writing of this paper. After consultation, Professor Jun Xian agreed to remove his name and therefore requests withdrawal of the manuscript