多重积分的一种近似计算方法——统计试验法  

An Approximate Calculation Method for Multi-integral——Monte Carlo Method

作　　者：方焱蕾 

机构地区：[1]宁波外事学校,浙江宁波315020

出　　处：《浙江工商职业技术学院学报》2007年第1期55-60,共6页Journal of Zhejiang Business Technology Institute

摘　　要：统计试验法是一种采用统计抽样理论近似地求解问题的方法。它的主要理论基础是概率论中的大数定理,其主要手段是随机变量的抽样。定积分的常用近似计算方法都不适用于多重积分,本文介绍统计试验法是如何有效地解决了这一问题,它具有计算方法及程序结构简单、收敛的概率性和收敛速度与问题的维数无关、适应性强等优点。Monte Carlo Method is a method seeking the answer by adopting sampling statistics. Its main theoretical base is the law of large numbers in the theory of probability, whose main means is the sampling of random variable. The usual approximate calculation method on definite integral doesn＇t fit for the multi-integral. This essay reports how the Monte Carlo Method can solve the problem effectively. Monte Carlo Method has quite a few advantages such as simplicity in calculation and procedure structure, no relation between convergent probability and convergent speed and the dimension of the problem, excellent adaptability and so on.

关 键 词：大数定理 统计抽样 平均值法 随机数 

分 类 号：O172.2[理学—数学]