2019/11/26 by Shigeki Aida, Aida, Shigeki, Nobuaki Naganuma +1
Economics, Econometrics and Finance · Mathematics · #60F05 #60G15 #60H35 #Differential Equations and Numerical Methods #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · doi:10.48550/arxiv.1911.11402
openalex publication_date 2019/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study asymptotic error distributions associated with standard approximation scheme for one-dimensional stochastic differential equations driven by fractional Brownian motions. This problem was studied by, for instance, Gradinaru-Nourdin [6], Neuenkirch and Nourdin [14] and the second named author [13]. The aim of this paper is to extend their results to the case where the equations contain drift terms and simplify the proof of estimates of the remainder terms in [13]. To this end, we represent the approximation solution as the solution of the equation which is obtained by replacing the fractional Brownian path with a perturbed path. We obtain the asymptotic error distribution as a directional derivative of the solution by using this expression.