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3
Superefcient Monte
Carlo Simulations
Cheng-An Yang, Kung Yao, Ken Umeno, and Ezio Biglieri
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 meth-
ods are widely used to solve complex engineering and scientic problems. Unlike other determinis-
tic 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 ...