Time reversal for drifted fractional Brownian motion with Hurst index H>1/2

Sébastien Darses (1) , Bruno Saussereau (2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

Let X be a drifted fractional Brownian motion with Hurst index H > 1/2. We prove that there exists a fractional backward representation of X, i.e. the time reversed process is a drifted fractional Brownian motion, which continuously extends the one obtained in the theory of time reversal of Brownian diffusions when H = 1/2. We then apply our result to stochastic differential equations driven by a fractional Brownian motion.

Mots clés: Fractional Brownian motion; Time reversal; Malliavin Calculus

Domaines: Probabilités [math.PR]

Sébastien Darses, Bruno Saussereau. Time reversal for drifted fractional Brownian motion with Hurst index H>1/2. Electronic Journal of Probability, 2007, 12, pp.1181-1211. ⟨hal-00485652⟩