It should be kept in mind though that this general description of Monte Carlo
methods may not directly apply to some applications. It is natural to think that
Monte Carlo methods are used to simulate random, or stochastic, processes,
since these can be described by pdf's. However, this coupling is actually too
restrictive because many Monte Carlo applications have no apparent
stochastic content, such as the evaluation of a definite integral or the inversion of a
system of linear equations. However, in these cases and others, one can pose
the desired solution in terms of pdf's, and while this transformation may seem
artificial, this step allows the system to be * treated* as a
stochastic process for
the purpose of simulation and hence Monte Carlo methods can be applied to
simulate the system. Therefore, we take a broad view of the definition of
Monte Carlo methods and include in the Monte Carlo rubric all methods that
involve statistical simulation of some underlying system, whether or not the
system represents a real physical process.

To illustrate the diversity of Monte Carlo methods, Figure 2 lists applications that have been addressed with statistical simulation techniques. As can be seen, the range of applications is enormous, from the simulation of galactic formation to quantum chromodynamics to the solution of systems of linear equations.

Figure 2: Monte Carlo Applicationts.

This wide diversity of methods is the reason that ``Monte Carlo is not Monte Carlo is not Monte Carlo.''