Pseudo-random sequences, quasi-random sequences for simulation

在许多应用科学中出现的数学模型太复杂，无法直接求解，因此必须使用数值近似来求解。不幸的是，随着问题中变量数量的增加，大多数数值逼近技术变得无效，因为达到规定精度水平所需的时间呈指数增长。蒙特卡罗方法是一种抽样技术，它试图通过产生合适的随机数并观察符合某种性质的数的分数来解决问题。对于中到高维度的问题，它们似乎表现得很好。许多蒙特卡罗问题最终都需要非均匀样本。这项研究的主要重点是寻找新的方法来产生多变量非均匀伪随机和准随机样本，这些样本具有适合于蒙特卡罗模拟的性质。

Mathematical models arising in many applied sciences are too complex to solve directly, and so must be solved using a numerical approximation. Unfortunately, as the number of variables in a problem increases, most numerical approximation techniques become ineffective, since the time required to reach a prescribed level of accuracy increases exponentially. Monte Carlo methods are a class of sampling techniques in which one attempts to solve a problem by generating suitable random numbers and observing the fraction of the numbers obeying some property. They seem to perform well for moderate to high-dimensional problems. Many Monte Carlo problems ultimately require non-uniform samples. The primary focus of this research is finding new methods to generate multivariate non-uniform pseudo-random and quasi-random samples with properties desirable for use with Monte Carlo simulations.