A Milstein-type scheme without Levy area terms for SDEs driven by fractional Brownian motion

Aurélien Deya; Andreas Neuenkirch; Samy Tindel

hal-00448685, version 1

A Milstein-type scheme without Levy area terms for SDEs driven by fractional Brownian motion

Aurélien Deya () ¹, Andreas Neuenkirch ², Samy Tindel () ^1, 3

Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques 48, 2 (2012) 518-550

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.

1: Institut Elie Cartan Nancy (IECN)
CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
2: Fakultät für Mathematik [Dortmund]
Technische Universität Dortmund
3: BIGS (INRIA Lorraine / IECN)
INRIA – CNRS : UMR7502

hal-00448685, version 1
http://hal.archives-ouvertes.fr/hal-00448685
oai:hal.archives-ouvertes.fr:hal-00448685
From: Samy Tindel <>
Submitted on: Tuesday, 19 January 2010 17:09:05
Updated on: Wednesday, 12 December 2012 05:49:47

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arXiv: 1001.3344

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