Variance reduction using antithetic variables for a nonlinear convex stochastic homogenization problem
Frédéric Legoll, William Minvielle · Discrete and Continuous Dynamical Systems - S · 2014
We consider a nonlinear convex stochastic homogenization problem, in astationary setting. Inpractice, the deterministic homogenized energy density isapproximated by a random apparent energy density, obtained by solving thecorrector problem on a truncated domain. We show that the technique of antithetic variables can be used to reducethe variance of the computed quantities, and thereby decrease thecomputational cost at equal accuracy. This leads to an efficientapproach for approximating expectations of the apparent homogenizedenergy density and of related quantities. The efficiency of the approach is numerically illustrated on severaltest cases. Some elements of analysis are also provided.