ABSTRACT
The Monte Carlo method (MCM), also known as the method of statistical trials, is the marriage of two major branches of theoretical physics: the probabilistic theory of random process dealing with Brownian motion or random-walk experiments and potential theory, which studies the equilibrium states of a homogeneous medium. MCMs are applied in two ways: simulation and sampling. Simulation refers to methods of providing mathematical imitation of real random phenomena. The simulation of any process or system in which there are inherently random components requires a method of generating or obtaining numbers that are random. Examples of such simulation occur in random collisions of neutrons, in statistics, in queueing models, in games of strategy, and in other competitive enterprises. An underlying concept of the probabilistic or Monte Carlo solution of differential equations is the random walk. Different types of random walk lead to different MCMs. The most popular types are the fixed-random walk and floating random walk.
