In this paper we introduce a control variate estimator for a quantity of interest that can be expressed as the expectation of a function of a random process, that is itself the solution of a differential equation driven by fast mean-reverting ergodic random forces. The control variate is built with the same function and with the limit diffusion process that approximates the original random process when the mean reversion time of the driving forces goes to 0. We propose a coupling of the original process and the limit diffusion process that gives a control variate estimator with small variance. We show that the correlation between the two processes indeed goes to 1 when the mean reversion time goes to 0 and we quantify the convergence rate, which allows us to characterize the variance reduction of the proposed control variate estimator. The efficiency of the method is illustrated on a few examples. © 2021 Wiley Periodicals LLC.

中文翻译：

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一种由扩散逼近驱动的控制变量法

在本文中，我们介绍了一个感兴趣量的控制变量估计器，它可以表示为随机过程函数的期望，它本身就是由快速均值恢复遍历随机力驱动的微分方程的解。控制变量是用相同的函数和极限扩散过程构建的，当驱动力的平均反转时间变为0时，该过程近似于原始随机过程。我们提出了原始过程和极限扩散过程的耦合，它给出了一个具有小方差的控制变量估计器。我们表明，当平均回归时间变为0时，两个过程之间的相关性确实变为1我们量化了收敛速度，这使我们能够描述所提出的控制变量估计器的方差减少。该方法的效率通过几个例子来说明。© 2021 威利期刊有限责任公司。