LAN property for stochastic differential equations with additive fractional noise and continuous time observation

Eulalia Nualart, Samy Tindel

Published 2015-08-31Version 1

We consider a stochastic differential equation with additive fractional noise of Hurst parameter $H>1/2$, and a non-linear drift depending on an unknown parameter. We show the Local Asymptotic Normality property (LAN) of this parametric model with rate $\sqrt{\tau}$ as $\tau\rightarrow \infty$, when the solution is observed continuously on the time interval $[0,\tau]$. The proof uses ergodic properties of the equation and a Poincar\'e type inequality.