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April 2020 Error analysis for approximations to one-dimensional SDEs via the perturbation method
Shigeki Aida, Nobuaki Naganuma
Osaka J. Math. 57(2): 381-424 (April 2020).

Abstract

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.

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Shigeki Aida. Nobuaki Naganuma. "Error analysis for approximations to one-dimensional SDEs via the perturbation method." Osaka J. Math. 57 (2) 381 - 424, April 2020.

Information

Published: April 2020
First available in Project Euclid: 6 April 2020

zbMATH: 07196683
MathSciNet: MR4081737

Subjects:
Primary: 60F05, 60G15, 60H35

Rights: Copyright © 2020 Osaka University and Osaka City University, Departments of Mathematics

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Vol.57 • No. 2 • April 2020
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