The Monte Carlo Method: Basic Principles
The main idea of the Monte Carlo method is to approximate an expected value E (X) by an arithmetic average of the results of a big number of independent experiments which all have the same distribution as X . The basis of this method is one of the most celebrated results of probability theory, the strong law of large numbers. As expected values play a central role in various areas of applications of probabilistic modelling, the Monte Carlo method has a widespread use. Examples of such areas of application are the analysis and design of queueing systems (such as in supermarkets or in large factories), the design of evacuation schemes for buildings, the analysis of the reliability of technical systems, the design of telecommunication networks, the estimation of risks of investments or of insurance portfolios, just to name a few.