On the minmax theory of estimating solutions of abstract parabolic equations. (English. Russian original) Zbl 0855.49016
Cybern. Syst. Anal. 31, No. 4, 626-630 (1995); translation from Kibern. Sist. Anal. 1995, No. 4, 169-175 (1995).
The authors obtain observation-dependent estimates for the quantities connected with solutions to evolution equations in Hilbert spaces. It is assumed that the observations depend on realization of stochastic processes with unknown second moment.
The properties of these estimates are studied and the minimax standard errors are evaluated.
The properties of these estimates are studied and the minimax standard errors are evaluated.
Reviewer: D.Palagachev (Sofia)
MSC:
| 49K35 | Optimality conditions for minimax problems |
| 49K20 | Optimality conditions for problems involving partial differential equations |
| 35K85 | Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators |
| 93E10 | Estimation and detection in stochastic control theory |
| 34G10 | Linear differential equations in abstract spaces |
References:
| [1] | V. L. Girko, S. I. Lyashko, and A. G. Nakonechnyi, ”Minmax controllers for evolution equations,” Kibernetika, No. 1, 67–68 (1987). |
| [2] | A. G. Nakonechnyi, Minmax Estimation of Functionals of Solutions of Variational Equations in Hilbert Spaces [in Russian], KGU, Kiev (1985). |
| [3] | B. N. Bublik, V. Ya. Danilov, and A. G. Nakonechnyi, Some Observation and Control Problems in Linear Systems [in Russian], KGU, Kiev (1988). |
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