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CONTROLO 2016 pp 253-263 | Cite as

Construction of Confidence Sets for Markov Chain Model

  • Dmitry ZavalishchinEmail author
  • Galina Timofeeva
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 402)

Abstract

The problem of forecasting the state probabilities vector for a stationary Markov chain with discrete time in case of transition probabilities are not exactly known and measured during the system operation is investigated. An auxiliary dynamic system with uncertainty and observation showing the dynamics of the state probabilities vector is constructed. Two approaches to the determination of the guaranteed with a given probability estimates are proposed. The first approach uses confidence sets for rows of the matrix of transition probabilities and the ellipsoidal calculus. The second approach is based on simulation and finding a sample quantile of an objective function, which determines the form of a confidence set for the system state.

Keywords

Markov chain Incomplete information Confidence estimate 

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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Department of Optimal ControlInstitute of Mathematics and Mechanics, Ural Branch of the Russian Academy of SciencesEkaterinburgRussia
  2. 2.Ural State University of Railway TransportEkaterinburgRussia
  3. 3.Ural Federal UniversityEkaterinburgRussia

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