Drift estimation with non-gaussian noise using Malliavin Calculus

Abstract

The aim of this paper is to show the existence of drift estimators dominating the standard one in continuous-time models of the form $X_{t}=u_{t}+Z_{t}$, where $u_{t}$ is the drift and $Z_{t}$ is either a Brownian martingale or a non-martingale noise living in the second Wiener chaos. Our results are based on the use of Malliavin calculus techniques, and extend previous findings of Privault and Réveillac (2008).