K-Antithetic Variates in Monte Carlo Simulation

. Standard Monte Carlo simulation needs prohibitive time to achieve reasonable estimations. for untractable integrals (i.e. multidimensional integrals and/or intergals with complex integrand forms). Several statistical technique, called variance reduction methods, are used to reduce the simulation time. In this note, we propose a generalization of the well known antithetic variate method. Principally we propose a K antithetic variate estimator (KAVE) based on the generation of K correlated uniform variates. Some numerical examples are presented to show the improvenment of our proposition.