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A note on Gibbs representation

  • I. V. Evstigneev
Part II
  • 230 Downloads
Part of the Lecture Notes in Mathematics book series (LNM, volume 653)

Keywords

Random Field Markov Random Field Finite Subset Stochastic Geometry Representation Ofal 
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.

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References

  1. 1.
    Averintsev M.B. On a method of describing discrete parameter random fields. Problemy Peredachi Informatsii, 6 (1970) no 2, 100–108.MathSciNetGoogle Scholar
  2. 2.
    Preston C.J. Generalized Gibbs states and Markov random fields. Adv. Appl.Prob., 5 (1973), 242–261.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Castaing C. Sur les multi-applications mesurables, Rev.Fr.Inf.Rech.Op., 1 (1967), 3–34.MathSciNetzbMATHGoogle Scholar
  4. 4.
    Rockafellar R.T. Measurable dependence of convex sets and functions on parameters, J.Math.Anal.Appl., 28 (1969), 4–25.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Matheron G. Ensembles fermes aléatoires, ensembles semi-markoviens et polyèdres poissoniens, Adv.Appl.Prob., 4 (1972), 508–541.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Stochastic geometry, eds. E.F.Harding, D.G.Kendall, N.-Y., J.Wiley, 1974.Google Scholar
  7. 7.
    Kozlov O.K., Gibbsian description of point random fields, Teorija Verojatnostej i Primen., 21 (1976), 348–365.MathSciNetzbMATHGoogle Scholar
  8. 8.
    Fortet R., Kambouzia M. Ensembles aléatoires induits par une repartition ponctuelle aléatoire, C.r.Acad.Sci., 280, 21 (1975).MathSciNetzbMATHGoogle Scholar
  9. 9.
    Molchan G.M. L-Markovian Gaussian fields, Doklady AN SSSR, 215, no 5 (1974).Google Scholar
  10. 10.
    Newman C.M. The construction of stationary two-dimensional Markoff fields with an application to quantum field theory, J.Functional. Anal., 14 (1973), 44–61.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Meyer P.A. Probability and potentials, Blaisdell Publishing Company, Waltham-Toronto-London, (1966).zbMATHGoogle Scholar
  12. 12.
    Dobrushin R.L. Description of random fields by means of conditional probabilities and their regularity conditions, Teorija Verojatnostej i Primen., 13 (1968), 197–224.Google Scholar
  13. 13.
    Evstigneev I.V. The space 2X and Markov fields, Doklady AN SSSR, 230, no 1 (1976).Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • I. V. Evstigneev
    • 1
  1. 1.CEMI, USSR Academy of SciencesRussia

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