Maximum Likelihood Drift Estimation for Gaussian Process with Stationary Increments
Анотація
The paper deals with the regression model X_t = \theta t + B_t , t\in[0, T ],where B=\{B_t, t\geq 0\} is a centered Gaussian process with stationary increments.We study the estimation of the unknown parameter $\theta$ and establish the formula for the likelihood function in terms of a solution to an integral equation.Then we find the maximum likelihood estimator and prove its strong consistency. The results obtained generalize the known results for fractional and mixed fractional Brownian motion.
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