Introduction to Monte Carlo Methods

Abstract

AbstractThe Monte Carlo method is a technique for analyzing phenomena by means of computer algorithms that employ, in an essential way, the generation of random numbers. The Monte Carlo method was given its name by Stanislaw Ulam and John von Neumann, who invented the method to solve neutron diffusion problems at Los Alamos in the mid 1940s.Monte Carlo methods are widely used in mathematics, science, industry, commerce, and entertainment. They are at the heart of algorithms used to make predictions about stochastic processes, that is, phenomena having some random component. This includes the motion of microscopic particles in an environment, the generation and movement of data packets through networks, the arrival and servicing of vessels at a busy port, and hundreds of other processes about which people need answers. Random numbers are used directly in the transmission and security of data over the airwaves or along the Internet. A radio transmitter and receiver could switch transmission frequencies from moment to moment, seemingly at random, but nevertheless in synchrony with each other. The Internet data could be credit-card information for a consumer purchase, or a stock or banking transaction secured by the clever application of random numbers. And randomness is an essential ingredient in games of all sorts, computer or otherwise, to make for unexpected action and keen interest.KeywordsMonte Carlo MethodRandom Number GeneratorSample PathJoint DensityBasic ProbabilityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.