Exact rate of convergence of some approximation schemes associated to SDEs driven by a fractional Brownian motion

Andreas Neuenkirch (1) , Ivan Nourdin (2)

1 Department of Mathematics [Darmstadt]
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

In this paper, we derive the exact rate of convergence of some approximation schemes associated to scalar stochastic differential equations driven by a fractional Brownian motion with Hurst index H.

Mots clés: Fractional Brownian motion; Russo-Vallois integrals; Doss-Sussmann type transformation; Stochastic differential equations; Euler scheme; Crank-Nicholson scheme; Mixing law

Domaines: Probabilités [math.PR]

Andreas Neuenkirch, Ivan Nourdin. Exact rate of convergence of some approximation schemes associated to SDEs driven by a fractional Brownian motion. 2006. ⟨hal-00016415v3⟩