On minimax filtration of vector processes

  • M. P. Moklyachuk

Abstract

We study the problem of optimal linear estimation of the transformation $A\xi = \smallint _0^\infty< a(t), \xi ( - t) > dt$ of a stationary random process $ξ(t)$ with values in a Hilbert space by observations of the process $ξ(t) + η(t)$ for $t ⩽ 0$. We obtain relations for computing the error and the spectral characteristic of the optimal linear estimate of the transformation $Aξ$ for given spectral densities of the processes $ξ(t)$ and $η(t)$. The minimax spectral characteristics and the least favorable spectral densities are obtained for various classes of densities.
Published
25.03.1993
How to Cite
MoklyachukM. P. “On Minimax Filtration of Vector Processes”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 45, no. 3, Mar. 1993, pp. 389–397, https://umj.imath.kiev.ua/index.php/umj/article/view/5821.
Section
Research articles