Parameter estimation for Vasicek model driven by a general Gaussian noise

Abstract

This article develop an inference problem for Vasicek model driven by a general Gaussian process. We construct a least squares estimator and a moment estimator for the drift parameters of the Vasicek model, and we prove the consistency and the asymptotic normality. Our approach partially extended the result of Xiao and Yu for the case when noise is a fractional Brownian motion with Hurst parameter The strategy is to exploit the Garsia–Rodemich–Rumsey inequality since the theorem of Pickands cannot be used any more in our case.