# 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

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topDeya, 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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