Work

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

Year: 2019

Type: article

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.

Source: Osaka City University (Osaka City University)

DOI: 10.48550/arxiv.1911.11402

Authors: Aida, Shigeki, Naganuma, Nobuaki

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

Awards: Studies on convergence in law of random variables from the viewpoint of functional analysis, Study on several problems in inifinite dimensional analysis and stochastic analysis

OpenAlex ID: W2989582180

FWCI:

Cites: 16

Cited by: 1

Related to: 10