A Control Variate Method Driven by Diffusion Approximation

In this paper we examine a control variate estimator for quantity that can be expressed as the expectation of functional random process, is itself solution differential equation driven by fast mean-reverting ergodic forces. The same limit diffusion process approximates original when mean-reversion time goes to zero. To get an efficient estimator, propose coupling method build and process. We show correlation between two processes indeed one mean reversion zero quantify convergence rate, which makes it possible characterize variance reduction proposed method. efficiency illustrated on few examples.