Journal of Mathematical Sciences

, Volume 97, Issue 2, pp 3923–3931 | Cite as

Markov fields and their applications in economics

  • P. S. Knopov
Article

Abstract

Models of policy of companies on the market with competing technologies are considered. It is shown that the Gibbs random fields can serve as a convenient formalization for the investigation of such models. In this case the highly developed theory of Markov random fields can be used for analysis and choice of optimal strategies. Bibliography: 14 titles.

Keywords

Optimal Strategy Random Field Markov Random Field Convenient Formalization Markov Field 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. L. Dobrushin, “Gibbs random fields for lattice systems with pairwise interaction,”Funkts. Anal. Prilozh.,2, No. 4, 31–43 (1968).Google Scholar
  2. 2.
    R. L. Dobrushin, “Markov processes with a large number of locally interacting components: the existence of the limiting process and its ergodicity,”Probl. Peredachi Inf.,7, No. 2, 149–161 (1971).Google Scholar
  3. 3.
    Yu. K. Belyaev, Yu. I. Gromak, and V. A. Malyshev, “On invariant random Boolean fields,”Mat. Zametki,6, No. 5, 555–566 (1969).MathSciNetGoogle Scholar
  4. 4.
    T. Liggett,Interacting particle systems, Springer-Verlag, New York (1989).Google Scholar
  5. 5.
    Ya. G. Sinay,The theory of phase transitions [in Russian], Nauka, Moscow (1980).Google Scholar
  6. 6.
    V. A. Malyshev and R. A. Minlos,Gibbs random fields [in Russian], Nauka, Moscow (1985).Google Scholar
  7. 7.
    D. Ruelle,Statistical mechanics, W. A. Benjamin, New York-Amsterdam (1969).Google Scholar
  8. 8.
    W. G. Sullivan,Markov processes for random fields, Dublin Institute for Advanced Studies, Dublin (1975).Google Scholar
  9. 9.
    M. B. Averintsev, “Description of Markov random fields by Gibbs conditional probabilities,”Teor. Veroyatn. Primen.,17 (1972).Google Scholar
  10. 10.
    N. B. Vasil'ev and O. K. Kozlov, “Markov chains with local interaction,” in:Multicomponent Stochastic Systems [in Russian], Nauka, Moscow (1978), pp. 83–100.Google Scholar
  11. 11.
    P. A. David and D. Foray, “Percolation structures, Markov random fields. The economics and eddy standards diffusion” (1992), Center for Economical Policy Research, Stanford University.Google Scholar
  12. 12.
    O. N. Stavskaya, “Gibbs invariant measures for Markov chains on finite lattices with local interaction,”Mat. Sb.,92, No. 3, 402–419 (1971).Google Scholar
  13. 13.
    C. Derman, “Stable sequential control rules and Markov chains,”J. Math. Anal. Appl.,6, 257–265 (1963).CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    C. Derman, “Markovian sequential decision processes,”Proc. Symposia Appl. Math.,16, 281–289 (1964).MATHMathSciNetGoogle Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • P. S. Knopov

There are no affiliations available

Personalised recommendations