Description
We consider stochastic processes that are the solution of the mixed stochastic differential equations involving both fractional Brownian and Wiener component.
Note that the model is rather flexible and can be applied for the
description of technical, economical and other real processes. Fractional Brownian motion is a component that is responsible for the so-called "long-memory phenomena" that is observed in the functioning of devices that provide cellular communication and many other devices.
We propose different statistical estimators of the unknown drift parameter and compare their properties. The construction of the estimators depends on whether the Wiener diffusion coefficient is zero or non-vanishing. In the first case we can consider maximum likelihood estimator, in the second case the situation is more involved. Discretization of observations and mutifractional processes are considered as well.