Antithetic Variates, Multivariate Dependence and Simulation of Stochastic Systems

Some theoretical and practical aspects antithetic and common random numbers for variance reduction in simulation of stochastic systems with dependent elements are considered. A proof of their optimality in estimating the expected value of the response sum or the response difference of a pair of functions of vector arguments with dependent components is presented. The efficiency of antithetic and common random numbers for variance reduction under different assumptions for the response functions is discussed. Applications to reliability, networks and queueing systems are given.