Parameter Estimation for Gaussian Processes with Application to the Model with Two Independent Fractional Brownian Motions

Abstract

The purpose of the article is twofold. Firstly, we review some recent results on the maximum likelihood estimation in the regression model of the form X t = θ G(t) + B t , where B is a Gaussian process, G(t) is a known function, and θ is an unknown drift parameter. The estimation techniques for the cases of discretetime and continuous-time observations are presented. As examples, models with fractional Brownian motion, mixed fractional Brownian motion, and sub-fractional Brownian motion are considered. Secondly, we study in detail the model with two independent fractional Brownian motions and apply the general results mentioned above to this model.

Parameter estimation for fractional mixed fractional Brownian motion based on discrete observations

“…An approach to parameter estimation based on the numerical solution to this equation was recently proposed in [21]. Estimation of the drift parameter by discrete observations was discussed in [20]. In Refs.…”