| 1. | Chapter 1 and 2 are the basic knowledge to use monte carlo and quasi - monte carlo methods . chapter 1 presents the error bounds of monte carlo and quasi - monte carlo integration methods
第1章和第2章是关于蒙特卡罗和拟蒙特卡罗方法的预备知识。 |
| 2. | 1 have studied a couple of topics on monte carlo and quasi - monte carlo methods . this dissertation covers its applications in integration , optimization and simulation
此论文主要阐述蒙特卡罗和拟蒙特卡罗方法在积分、优化和模拟方面的应用的若干主题。 |
| 3. | Because the random numbers generators are the key of monte carlo methods and quasi - monte carlo methods . chapter 2 describes the pseudo - random number generators and quasi - random number generators
因为随机数发生器是蒙特卡罗和拟蒙特卡罗方法的核心之一，所以第2章介绍了伪随机数和拟随机数发生器。 |
| 4. | We use genetic programming to optimize the the right hand functions of the ordinary differential equations . adaptive quasi - monte carlo optimization methods are used to optimize the coefficients of the functions
我们用遗传程序设计方法优化常微分方程右端的函数，用自适应拟蒙特卡罗优化方法优化函数中的系数。 |
| 5. | In this paper , we use computer to generate pseudo random number and low - discrepancy sequences . on this foundation , monte carlo integration and quasi - monte carlo integration are researched
摘要在本文中，我们利用计算机分别产生了伪随机数序列和低差异数序列。在此基础上，我们研究了蒙特卡罗积分与拟蒙特卡罗积分。 |
| 6. | The standard rejection sampling method which is introduced in chapter 2 is closely related to the problem of quasi - monte carlo integration of characteristic functions , whose accuracy may be lost due to the discontinuity of the characteristic functions
第2章介绍的标准拒绝抽样方法其实跟特征函数的蒙特卡罗积分有密切的关系。而由于特征函数的不连续性，蒙特卡罗积分应有的误差精度就达不到，拒绝抽样的效果也就受到影响。 |
| 7. | By comparing these two methods , we show the advantages of quasi - monte carlo method . we also introduce the standard monte carlo random search for optimization . the last but not least application is metropolis algorithms which is the origin of monte carlo method
第1章介绍了蒙特卡罗和拟蒙特卡罗积分的误差估计并阐述了拟蒙特卡罗方法的优势，同时介绍了拟蒙特卡罗的标准优化方法，最后介绍了蒙特卡罗方法的起源? metropolis模拟方法。 |
| 8. | We apply the b - spline smoothed rejection sampling method to importance sampling . numerical experiments show that the error size o ( n - 1 ) is regained by using the b - spline smoothed rejection method for quasi - monte carlo estimate . the error bound of monte carlo method using b - spline smoothed importance sampling is also better than that of the standard monte carlo method
将b样条光滑拒绝方法用于重要抽样估计，数值例子显示拟蒙特卡罗积分的精度重新达到了o ( n ~ ( - 1 ) )的阶，而对于蒙特卡罗积分，采用b样条光滑重要抽样，其精度也比标准积分的精度o ( n ~ ( - 2 / 1 ) )好。 |
