Estimation in models driven by fractional Brownian motion

Classification: 60F05; 60G15; 60G18; 60H10; 62F03; 62F12; 33C45International audienceLet $\{b_{H}(t), t\in \mathbb R\}$ be the fractionalBrownian motion with parameter $0 In different particular models where $\sigma(x)=\sigma$ or $\sigma(x)=\sigma \, x$ and $\mu(x)=\mu$ or $\mu(x)=\mu \, x$, we propose a central limit theorem for estimators of $H$ and of $\sigma$based on regression methods. Then we give tests of hypothesis on $\sigma$ for these models.We also consider functional estimation on $\sigma(\cdot)$ in the above more general models based in the asymptotic behavior of functionals of the $2^{nd}$-order increments of the fBm