A Milstein-type scheme without Levy area terms for SDEs driven by fractional Brownian motion
Probability
2015-05-18 v1
Abstract
In this article, we study the numerical approximation of stochastic differential equations driven by a multidimensional fractional Brownian motion (fBm) with Hurst parameter greater than 1/3. We introduce an implementable scheme for these equations, which is based on a second order Taylor expansion, where the usual Levy area terms are replaced by products of increments of the driving fBm. The convergence of our scheme is shown by means of a combination of rough paths techniques and error bounds for the discretisation of the Levy area terms.
Keywords
Cite
@article{arxiv.1001.3344,
title = {A Milstein-type scheme without Levy area terms for SDEs driven by fractional Brownian motion},
author = {Aurélien Deya and Andreas Neuenkirch and Samy Tindel},
journal= {arXiv preprint arXiv:1001.3344},
year = {2015}
}