A0830
Title: Drift estimation for rough processes under small noise asymptotic: QMLE approach
Authors: Arnaud Gloter - Universite d Evry Val d Essonne (France) [presenting]
Nakahiro Yoshida - University of Tokyo (Japan)
Abstract: The purpose is to consider a process $X$ solution of a stochastic Volterra equation with an unknown parameter $\theta$ in the drift function. The Volterra kernel is singular and given by $K(u)=c u^{\alpha-1}$ with $\alpha \in (1/2,1)$, and it is assumed that the diffusion coefficient is proportional to $\epsilon \to 0$. Based on the observation of a discrete sampling with mesh $h$ of the Volterra process, a quasi maximum likelihood estimator is built. The main step is to assess the error arising in the reconstruction of the path of a semi-martingale from the inversion of the Volterra kernel. It is shown that this error decreases as $h^{1/2}$, whatever is the value of $\alpha$. Then, an explicit contrast function can be introduced, which yields an efficient estimator when $\epsilon \to 0$.
