Monte Carlo method

Summary

A Monte Carlo method computes a deterministic quantity approximately by drawing random samples. In its basic form the quantity is the expected value of a random variable. It is estimated by the average of many independent copies. The law of large numbers makes the estimate converge. The central limit theorem shows that the error decreases like $1/\sqrt{n}$ for $n$ samples, whatever the dimension. This makes Monte Carlo methods the tool of choice for integrals in high dimension and for complex stochastic models.