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

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

1 IECN - Institut Élie Cartan de Nancy
2 Fakultät für Mathematik [Dortmund]
3 BIGS - Biology, genetics and statistics

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.

Mots clés: Levy area; Approximation schemes; Fractional Brownian motion

Domaines: Probabilités [math.PR]

Aurélien Deya, Andreas Neuenkirch, Samy Tindel. A Milstein-type scheme without Levy area terms for SDEs driven by fractional Brownian motion. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2012, 48 (2), pp.518-550. ⟨10.1214/10-AIHP392⟩. ⟨hal-00448685⟩