Quasi-Monte Carlo methods are a way of improving the efficiency of Monte Carlo methods. Digital nets and sequences are one of the low discrepancy point sets used in quasi-Monte Carlo methods. This thesis presents the three new results pertaining to digital nets and sequences: implementing randomized digital nets, finding the distribution of the discrepancy of scrambled digital nets, and obtaining better quality of digital nets through evolutionary computation. Finally, applications of scrambled and non-scrambled digital nets are provided.
翻译:“准蒙卡罗”方法是提高蒙特卡洛方法效率的一种方法,数字网和序列是半蒙卡罗方法中使用的低差点数据集之一,它提出了与数字网和序列有关的三个新结果:执行随机数字网,找出拼凑数字网的分布,通过渐进计算提高数字网的质量;最后,提供拼凑和非拼凑数字网的应用。