Minimax a posteriori estimation in the hidden Markov models
- 30 Downloads
Consideration was given to the minimax estimation in the observation system including a hidden Markov model for continuous and counting observations. The dynamic and observation equations depend on a random finite-dimensional parameter having an unknown distribution with the given support. The conditional expectation of the available observation of some generalized quadratic loss function was used as the risk function. Existence of the saddle point in the formulated minimax problem was proved, and the worst distribution and the minimax estimate as the solution of a simpler dual problem were characterized.
Unable to display preview. Download preview PDF.
- 1.Kats, I.Ya. and Kurzhanskii, A.B., Minimax Multistep Filtration in the Statistically Uncertain Situations, Avtom. Telemekh., 1978, no. 11, pp. 79–87.Google Scholar
- 3.Anan’ev, B.I., Minimax Linear Filtration of the Multistep Processs with Uncertain Distribution of Perturbations, Avtom. Telemekh., 1993, no. 10, pp. 131–139.Google Scholar
- 5.Borisov, A.V., Preliminary Analysis of the Distribution of States of the Randomly Structured Special-purpose Controlled Systems, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2005, no. 1, pp. 48–62.Google Scholar
- 9.Liptser, R.Sh. and Shiryaev, A.N., Statistika sluchainykh protsessov, Moscow: Nauka, 1974. Translated into English under the title Statistics of Random Processes, Berlin: Springer, 1978.Google Scholar
- 10.Borisov, A.V., Analysis of the States of the Hidden Markov Processes Generated by the Special Jump Processes, Teor. Veroyatn. Primen., 2006, no. 3, pp. 589–600.Google Scholar
- 11.Ladyzhenskaya, O.A., Solonnikov, V.A., and Ural’tseva, N.N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa (Linear and Quasilinear Parabolic Equations), Moscow: Nauka, 1967.Google Scholar
- 13.Pardoux, E., Filtering of a Diffusion Process with Poisson Type Observation, in Stochastic Control Theory and Stochastic Differential Equations. Lecture Notes in Control and Information Sciences, 1979, vol. 16.Google Scholar
- 14.Semenikhin, K.V., Minimax Estimation of the Random Elements by the RMS Criterion, Teor. Veroyatn. Primen., 2003, no. 5, pp. 12–25.Google Scholar