Maximum likelihood estimator for the sub-fractional Brownian motion approximated by a random walk

We estimate the drift parameter in a simple linear model driven by sub-fractional Brownian motion. We construct a maximum likelihood estimator (MLE) for the drift parameter by using a random walk approximation of the sub-fractional Brownian motion and study the asymptotic behaviors of the estimator. Simulations confirm the theoretical results and indicate superiority of the new proposed estimator. Copyright The Institute of Statistical Mathematics, Tokyo 2015