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Conditions for Gaussian homogeneous fields to belong to classes

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This paper is the continuation of [1], [2]. In it questions of approximation of functions are discussed, when a realization of the homogeneous Gaussian field belongs to the class H rp (G)0.

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References

  1. I. A. Ibragimov, "Properties of realizations of random processes, and imbedding theorems," Teor. Veroyatn. Primenen.,18, No. 3, 468–480 (1973).

    Google Scholar 

  2. I. A. Ibragimov, "On conditions for the smoothness of trajectories of random functions," Teor. Veroyatn. Primenen.,28, No. 2, 229–250 (1983).

    Google Scholar 

  3. B. S. Cirel'son, I. A. Ibragimov, and V. N. Sudakov, "Norms of Gaussian sample functions," in: Proc. Third Japan-USSR Symposium on Probability Theory, Lecture Notes in Math., No. 550, Springer, Berlin (1976), pp. 20–41.

    Google Scholar 

  4. S. M. Nikol'skii, Approximation of Functions of Several Variables and Imbedding Theorems, Springer, New York (1975).

    Google Scholar 

  5. V. N. Sudakov and B. S. Tsirel'son, "Extremal properties of semispaces for spherically invariant measures," Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,41, 14–24 (1974).

    Google Scholar 

  6. W. Feller, An Introduction to Probability Theory and Its Applications, Vol. I, Wiley, New York (1968).

    Google Scholar 

  7. A. V. Skorokhod, "A note on Gaussian measures in Banach space," Teor. Veroyatnost. i Primenen.,15, No. 3, 519–520 (1970).

    Google Scholar 

  8. V. V. Buldygin, The Convergence of Random Elements in Topological Spaces [in Russian], Naukova Dumka, Kiev (1980).

    Google Scholar 

  9. N. I. Akhiezer, Lectures in the Theory of Approximation [in Russian], Nauka, Moscow (1965).

    Google Scholar 

  10. T. W. Anderson, "The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities," Proc. Amer. Math. Soc.,6, 170–176 (1955).

    Google Scholar 

  11. A. Ehrhard, "Symmétrisation dans l'espace de Gauss," Math. Scand.,53, 281–301 (1983).

    Google Scholar 

  12. M. Nisio, "On the continuity of stationary Gaussian processes," Nagoya Math. J.,34, 89–104 (1969).

    Google Scholar 

  13. E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals, Clarendon Press, Oxford (1948).

    Google Scholar 

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Authors
  1. I. A. Ibragimov
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 184, pp. 126–143, 1990.

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Ibragimov, I.A. Conditions for Gaussian homogeneous fields to belong to classes. J Math Sci 68, 484–497 (1994). https://doi.org/10.1007/BF01254273

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