Some Methods for the Exact Estimation of a~Parameter of a~Gaussian Stohastic Process

V. G. Alekseev

Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 3, pp. 516-519

Résumé

The paper deals with stochastic processes $\xi(t)$ and $\eta(t)$, $0\leqq t\leqq T$, having stationary Gaussian increments, zero means and spectral densities $f_\xi(\lambda)$ and $f_\eta(\lambda )=f_\xi(\lambda)+cf_\zeta(\lambda)$, respectively, where $f_\xi(\lambda)$ and $f_\zeta(\lambda)$ are known non-negative functions, and $c\geqq 0$ is an unknown parameter. It is assumed that the Gaussian measures in the function space corresponding to the processes $\xi(t)-\xi(0)$ and $\eta(t)-\eta(0)$ are orthogonal for $c>0$. We give the functionals of sample functions of the process $\eta(t)$ which could be used for the exact determination of the parameter $c$.