Méthode de simulation avec les variables antithétiques
In this master thesis, we consider simulation methods based on antithetic variates for estimate integrales of f(x) on interval (0,1] where f is monotonic function, not a monotonic function or a function difficult to integrate.  The main idea consists in subdividing the (0,1] in m sections of which each one is subdivided in l subintervals. This method is done recursively. At each step the variance decreases, i.e. The variance obtained at the kth step is smaller than that is found at the (k-1)th step. This allows us to reduce the error in the estimation because the estimator of integrales of f(x) on interval [0,1] is unbiased. The objective is to optimize m.
Unbiased estimator Random numbers Monte Carlo simulation Antithetic variates Variance reduction