Exact convergence rate of the Wong–Zakai approximation to RDEs driven by Gaussian rough paths. Issue 7 (2nd October 2016)

• Record Type: Journal Article
• Authors: Naganuma, Nobuaki
• Is Part Of: Stochastics. Volume 88:Issue 7(2016)
• Page Start: 1041
• Page End: 1059
• Publication Date: 2016-10-02
• Subjects: Rough path -- the Wong–Zakai approximation -- convergence rate -- Gaussian process -- fractional Brownian motion; 60H35 -- 60H10 -- 60G15; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2016.1178750
• Languages: English
• ISSNs: 1744-2508

Abstract

Abstract : We consider a solution to a stochastic differential equation driven by a Gaussian process in the rough differential equation sense and the Wong–Zakai approximation to the solution. We give an upper bound of the error of the Wong–Zakai approximation. We also show that the upper bound is optimal in a particular case.