A note on inference for the mixed fractional Ornstein-Uhlenbeck process with drift

This paper is devoted to the controlled drift estimation of mixed fractional Ornstein-Uhlenbeck process. We will consider two models: one optimal input where we find function which maximize Fisher information for unknown parameter and other with a constant as function. Large sample asymptotical properties Maximum Likelihood Estimator (MLE) deduced using Laplace transform computations or Cameron-Martin formula extra part from [ 12 ]. As supplement ] also prove that MLE strongly consistent.