Maximum likelihood estimation for Gaussian process with nonlinear drift

. We investigate the regression model Xt = θG(t) + Bt, where θ is an unknown parameter, G is a known nonrandom function, and B is a centered Gaussian process. We construct the maximum likelihood estimators of the drift parameter θ based on discrete and continuous observations of the process X and prove their strong consistency. The results obtained generalize the paper [13] in two directions: the drift may be nonlinear, and the noise may have nonstationary increments. As an example, the model with subfractional Brownian motion is considered.