Milstein's type schemes for fractional SDEs

Mihai Gradinaru (1) , Ivan Nourdin (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

Weighted power variations of fractional Brownian motion B are used to compute the exact rate of convergence of some approximating schemes associated to one-dimensional stochastic differential equations (SDEs) driven by B. The limit of the error between the exact solution and the considered scheme is computed explicitly.

Mots clés: exact rate of convergence; Fractional Brownian motion; weighted power variations; stochastic differential equation; approximating scheme; exact rate of convergence.

Domaines: Probabilités [math.PR]

Mihai Gradinaru, Ivan Nourdin. Milstein's type schemes for fractional SDEs. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2009, 45 (4), pp.1085-1098. ⟨10.1214/08-AIHP196⟩. ⟨hal-00130399v3⟩