The Monte Carlo Method And Application

Monte Carlo method, sometimes called the statistical simulation method or the random sampling technique, based on "random" and the theory of probability and statistics, has been widely used as a very important numerical calculation method.By virtue of the rapidly developed computer as a platform and the scientific and reasonable statistical modeling, the Monte Carlo method translates the complex studied object or computational problems into random numbers and its characteristics for simulation and calculation,which thus simplifies the research problem essentially, reduces the computational complexity and gets the good properties of approximate solution.This paper briefly expounds the formation, development and application of Monte Carlo method, introducing the basic idea, principle and characteristics of Monte Carlo method, including convergence, error, advantages and disadvantages, and even the way how to apply the Monte Carlo method. Combined with the instance, The third chapter of this article illustrates how the Monte Carlo method works for different types of problems.Portfolio includes the calculation of irrational Numbers, definite integral and oil storage of gas station, the optimization problems of power-up of workshop, and the problem of DVD for lease. What is more, this paper fully introduces the steps that how the Monte Carlo method is to be achieved, completing with codes made by Matlab, which reflects the Monte Carlo method is widely applicable with good properties of high efficiency.Especially the problem of calculating of oil storage tanks, makes clear that the convergence and convergence rate of the Monte Carlo method have nothing to do with the problem of dimension, and even the Monte Carlo has a unique advantage dealing with the problem of high-dimensional.At last, the fourth chapter of this article, introduces a kind of parameters interval estimation method based on Monte Carlo algorithm, and in the case of exponential distribution, implements the method and two traditional algorithm of single parameter interval estimation, gets30groups of interval estimation from different samples of the same confidence level and18groups of interval estimation from the same samples of different confidence level. And then with a large number of calculations, comparing the scope of application, the advantages and disadvantages of the methods with two kinds of traditional methods in this paper, some correlation analysis and conclusions are obtained.