A Milstein-type scheme without Lévy area terms for SDEs driven by fractional brownian motion

A. Deya; A. Neuenkirch; S. Tindel

Annales de l'I.H.P. Probabilités et statistiques (2012)

  • Volume: 48, Issue: 2, page 518-550
  • ISSN: 0246-0203

Abstract

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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 Lévy 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 discretization of the Lévy area terms.

How to cite

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Deya, A., Neuenkirch, A., and Tindel, S.. "A Milstein-type scheme without Lévy area terms for SDEs driven by fractional brownian motion." Annales de l'I.H.P. Probabilités et statistiques 48.2 (2012): 518-550. <http://eudml.org/doc/272092>.

@article{Deya2012,
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 Lévy 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 discretization of the Lévy area terms.},
author = {Deya, A., Neuenkirch, A., Tindel, S.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {fractional brownian motion; Lévy area; approximation schemes; fractional Brownian motion},
language = {eng},
number = {2},
pages = {518-550},
publisher = {Gauthier-Villars},
title = {A Milstein-type scheme without Lévy area terms for SDEs driven by fractional brownian motion},
url = {http://eudml.org/doc/272092},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Deya, A.
AU - Neuenkirch, A.
AU - Tindel, S.
TI - A Milstein-type scheme without Lévy area terms for SDEs driven by fractional brownian motion
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2012
PB - Gauthier-Villars
VL - 48
IS - 2
SP - 518
EP - 550
AB - 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 Lévy 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 discretization of the Lévy area terms.
LA - eng
KW - fractional brownian motion; Lévy area; approximation schemes; fractional Brownian motion
UR - http://eudml.org/doc/272092
ER -

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