Least squares estimator for a class of subdiffusion processes

In this article, we consider the parameter estimation problem for a class of subdiffusion processes which are characterized by the time-changed Ornstein-Uhlenbeck processes. Least squares method is used to obtain the estimator for the drift coefficient. First, we get the strong consistency, asymptotical normality and asymptotical mixed normality for the estimator on the condition that we can observe the process continuously. After that, weak consistent and asymptotic properties are derived basing on discrete observations when the time-change process is an inverse z-stable (4/5 < alpha < 1) subordinator.