Error analysis for approximations to one-dimensional SDEs via the perturbation method

Shigeki Aida; Nobuaki Naganuma

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arXiv · 1911.11402

Error analysis for approximations to one-dimensional SDEs via the perturbation method

Shigeki Aida·Nobuaki Naganuma

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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. 2019-11-26. Error analysis for approximations to one-dimensional SDEs via the perturbation method. https://arxiv.org/abs/1911.11402

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