General Principles of the Monte Carlo Method

Abstract

This chapter discusses the principles of the Monte Carlo method. The Monte Carlo method or method of statistical trials consists of solving various problems of computational mathematics by means of the construction of some random process for each such problem, with the parameters of the process equal to the required quantities of the problem. These quantities are determined approximately by means of observations of the random process and the computation of its statistical characteristics, which are approximately equal to the required parameters. For example, the required quantity x might be the mathematical expectation M ξ of a certain random variable. The Monte Carlo method for determining the approximate value of the quantity x consists of an N-fold sampling of the value of the variable ξ in a series of independent tests: ξ1, ξ2,…, ξN, and the computation of their mean value