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The problem of distinguishing among hypotheses for isotropic random fields

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Literature Cited

  1. 1.

    C. W. Helstrom, Statistical Theory of Signal Detection [Russian translation], IL, Moscow (1963).

  2. 2.

    W. B. Davenport, Jr. and W. L. Root, Introduction to the Theory of Random Signals and Noise [Russian translation], IL, Moscow (1960).

  3. 3.

    D. Middleton, Introduction to Statistical Communication Theory [Russian translation], Vols. 1, 2, Izd. Sovetskoe Radio, Moscow (1962).

  4. 4.

    B. R. Levin, Theoretical Foundations of Statistical Radio Engineering [in Russian], Book II, Izd. Sovetskoe Radio, Moscow (1968).

  5. 5.

    W. Grenander, Random Processes and Statistical Derivations [Russian translation], IL, Moscow (1961).

  6. 6.

    I. I. Gikhman and A. V. Skorokhod, “On the density of probabilistic measures in functional spaces,” Uspekhi Matem. Nauk,21, No. 6, (1966).

  7. 7.

    I. I. Gikhman and A. V. Skorokhod, Theory of Random Processes [in Russian], Vol. 1, Izd. Nauka, Moscow (1971).

  8. 8.

    P. S. Knopov, “Certain remarks on the checking of hypotheses for random fields,” Kibernetika, No. 6 (1966).

  9. 9.

    Z. S. Zerakidze, “On the equivalence of the distributions of Gaussian uniform fields,” in: Transactions of the Institute of Applied Mathematics, Tbilisi State University, Vol. 2 [in Russian] (1969).

  10. 10.

    M. I. Yadrenko, “On the absolute continuity of measures corresponding to Gaussian uniform random fields,” in: Probability Theory and Mathematical Statistics [in Russian], No. 7, Izd. Kievskogo Gosuniversiteta (1972).

  11. 11.

    A. V. Skorokhod and M. I. yadrenko, “On the absolute continuity of measures corresponding to random fields,” Teoriya Veroyatnostei i ee Primenenie,18, No. 1 (1973).

  12. 12.

    M. I. Yadrenko, “On a certain problem of linear extrapolation for an isotropic random field,” in: Probability Theory and Mathematical Statistics [in Russian], No. 1, Izd. Kievskogo Gosuniversiteta (1971).

  13. 13.

    H. Bateman and A. Erdelyi, Higher Transcendental Functions [Russian translation], Vol. II, Izd. Nauka, Moscow (1966).

  14. 14.

    M. I. Yadrenko, “Isotropic random fields of the Markovian type,” in: Probability Theory and Mathematical Statistics [in Russian], No. 5, Izd. Kievskogo Gosuniversiteta (1971).

  15. 15.

    Yu. A. Rozanov, “Gaussian finite-dimensional distributions,” in: Transactions of the V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR [in Russian], Vol. CVIII, Moscow (1968).

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Translated from Kibernetika, No. 5, pp. 68–72, September–October, 1975.

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Yadrenko, M.I. The problem of distinguishing among hypotheses for isotropic random fields. Cybern Syst Anal 10, 813–819 (1974). https://doi.org/10.1007/BF01069803

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Keywords

  • Operating System
  • Artificial Intelligence
  • System Theory
  • Random Field
  • Isotropic Random Field