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Parameter estimation for Gaussian processes with application to the model with two independent fractional Brownian motions
Yuliya Mishura, Kostiantyn Ralchenko, Sergiy Shklyar · 2018-08-25 · via math.PR updates on arXiv.org

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 $X_t = θG(t) + B_t$, 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 discrete-time 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.

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