ABSTRACT
Ulam and von Neumann rst formulated the Monte Carlo (MC) simulation methodology as one using random sequences to evaluate high-dimensional integrals. Since then, MC simulation methods are widely used to solve complex engineering and scientic problems. Unlike other deterministic methods, MC methods use statistical sampling to produce approximate solutions. A fundamental question of implementing MC simulation is how to generate random samples. It turned out that the generation of truly random sequences in a controlled manner is a nontrivial problem. Fortunately, in many applications, it sufces to use pseudorandom (PR) sequences. A PR sequence can be generated deterministically by some transformations, and it appears to be random from the statistical point of view. As the processed sample size N grows, the uncertainty of the MC solution is reduced. It is well known that the variance of the approximation error decreases as 1/N. However, for computationally intensive simulations, MC methods may take an extremely long number of samples to obtain a solution with acceptable tolerance.
