Asymptotic expansions at any time for fractional scalar SDEs of Hurst index H>1/2

Sébastien Darses (1) , Ivan Nourdin (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We study the asymptotic developments with respect to $h$ of E[D_h f(X_t)], E[D_h f(X_t)|F_t] and E[D_h f(X_t)|X_t], where D_h f(X_t)=f(X_{t+h})-f(X_t), when f:R->R is a smooth real function, t is a fixed time, X is the solution of a one-dimensional stochastic differential equation driven by a fractional Brownian motion of Hurst index H>1/2 and F is its natural filtration.

Mots clés: Asymptotic development; Fractional Brownian motion; stochastic differential equation; Malliavin calculus

Domaines: Probabilités [math.PR]

Sébastien Darses, Ivan Nourdin. Asymptotic expansions at any time for fractional scalar SDEs of Hurst index H>1/2. 2007. ⟨hal-00138773v2⟩