A Control Variate Method Driven by Diffusion Approximation. Issue 3 (14th January 2021)

• Record Type: Journal Article
• Authors: Garnier, Josselin; Mertz, Laurent
• Is Part Of: Communications on pure and applied mathematics. Volume 75:Issue 3(2022)
• Page Start: 455
• Page End: 492
• Publication Date: 2021-01-14
• Subjects: Mathematics -- Periodicals; Mechanics -- Periodicals; Mathématiques -- Périodiques; Mécanique -- Périodiques; 510.5
• DOI: 10.1002/cpa.21976
• Languages: English
• ISSNs: 0010-3640

Abstract

Abstract: 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.