Reliable Computing

, Volume 8, Issue 2, pp 97–113 | Cite as

Interval-Valued Finite Markov Chains

  • Igor O. Kozine
  • Lev V. Utkin


The requirement that precise state and transition probabilities be available is often not realistic because of cost, technical difficulties or the uniqueness of the situation under study. Expert judgements, generic data, heterogeneous and partial information on the occurrences of events may be sources of the probability assessments. All this source information cannot produce precise probabilities of interest without having to introduce drastic assumptions often of quite an arbitrary nature. in this paper the theory of interval-valued coherent previsions is employed to generalise discrete Markov chains to interval-valued probabilities. A general procedure of interval-valued probability elicitation is analysed as well. In addition, examples are provided.


Mathematical Modeling Markov Chain Computational Mathematic General Procedure Industrial Mathematic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kemeny, J. G. and Snell, J. L.: Finite Markov Chains, Van Nostrand Reinhold Company, New York, 1960.Google Scholar
  2. 2.
    Kuznetsov, V. P.: Interval Statistical Models, Radio and Communication, Moscow, 1991 (in Russian).Google Scholar
  3. 3.
    Walley, P.: Measures of Uncertainty in Expert Systems, Artificial Intelligence 83 (1996), pp.1–58.Google Scholar
  4. 4.
    Walley, P.: Statistical Reasoning with Imprecise Probabilities, Chapman and Hall, London, 1991.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Igor O. Kozine
    • 1
  • Lev V. Utkin
    • 2
  1. 1.Systems Analysis DepartmentRisø National LaboratoryRoskildeDenmark
  2. 2.Department of Computer ScienceForest Technical AcademySt.PetersburgRussia

Personalised recommendations