Parameter estimations for the sub-fractional Brownian motion with drift at discrete observation

Abstract

In this paper, we investigate the $L^{2}$-consistency and the strong consistency of the maximum likelihood estimators (MLE) of the mean and variance of the sub-fractional Brownian motion with drift at discrete observation. By combining the Stein’s method with Malliavin calculus, we obtain the central limit theorem and the Berry–Esséen bounds for these estimators.