A Control Variate Method Driven by Diffusion Approximation - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Communications on Pure and Applied Mathematics Year : 2022

A Control Variate Method Driven by Diffusion Approximation

Abstract

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

Dates and versions

hal-03897282 , version 1 (13-12-2022)

Identifiers

Cite

Josselin Garnier, Laurent Mertz. A Control Variate Method Driven by Diffusion Approximation. Communications on Pure and Applied Mathematics, 2022, 75 (3), pp.455-492. ⟨10.1002/cpa.21976⟩. ⟨hal-03897282⟩
16 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More