On Asymptotic Properties of Some Statistical Estimates for Gaussian Stochastic Processes

The paper deals with stochastic process $\eta(t)$ $(0\le t\le T)$ having stationary Gaussian increments, zero mean and spectral density $f_\eta(\lambda)=f_\xi(\lambda)+cf_\zeta(\lambda)$ where $f_\xi(\lambda)$ and $f_\zeta(\lambda)$ are known non-negative functions and $c\ge0$ is an unknown parameter. It is shown, that the unbiased consistent; estimates of $с$ suggested in [1] are also asymptotically normal and asymptotically efficient when some unrestrictive conditions are imposed.