Modified Monte Carlo Methods Using Quasi-Random Sequences
Modified Monte Carlo Methods Using Quasi-Random Sequences
复制标题
使用准随机序列的改进蒙特卡罗方法
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
B. Moskowitz
中科院分区：
文献类型：
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作者：
R. Caflisch;B. Moskowitz
计算实验表明，使用拟随机序列的蒙特卡罗方法对于高维或被积函数不光滑的积分问题失去了一定的有效性。本文提出了两种改进的蒙特卡罗方法，它们具有更快的收敛速度。标准拒绝方法涉及不连续，对应于接受或拒绝的决定。取而代之的是，提出了一种平滑的拒绝方法，并发现该方法在用于准随机序列时非常有效。Feynman-Kac路径积分的蒙特卡罗计算涉及高维，每个离散时间间隔为一维。通过一种交替的离散化，大大降低了积分域的有效维度，使准随机序列是有效的。
Computational experiments have shown that Monte Carlo methods using quasi-random sequences lose some of their effectiveness for integration problems in which the dimension is large or the integrand is not smooth. In this paper, two modified Monte Carlo methods are developed, which regain an enhanced convergence rate. The standard rejection method involves discontinuities, corresponding to the decision to accept or reject. In place of this, a smoothed rejection method is formulated and found to be very effective when used with quasi-random sequences. Monte Carlo evaluation of Feynman-Kac path integrals involves high dimension, one dimension for each discrete time interval. Through an alternative discretization, the effective dimension of the integration domain is drastically reduced, so that quasi-random sequences are effective.