Least squares estimation for the drift parameters in the sub-fractional Vasicek processes

While the statistical inference of Vasicek processes driven by both Brownian motions and fractional Brownian motions has a long history, the statistical analysis for the Vasicek model driven by other fractional Gaussian processes is obviously more recent. This paper considers the parameter estimation problem for Vasicek processes driven by sub-fractional Brownian motions with the known Hurst parameter greater than one half. Since the maximum likelihood estimators are hardly analyzed because of the stochastic integrals with singular kernels, least squares estimators for drift parameters are provided based on time-continuous observations. The strong consistency results as well as the asymptotic distributions of these estimators are obtained in both the non-ergodic case and the null recurrent case.