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Regularity of sampling distribution functions of a random process

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Literature cited

  1. 1.

    B. Boulicaut, “Fonctions de Young et continuitè de trajectoires d'une, fonction aléatoire,” Ann. Inst. Fourier,24, No. 2, 27–47 (1974).

  2. 2.

    T. Karamata, “Sur un mode de croissance règuliere des fonctions,” Math. (Cluj),4, 38–53 (1930).

  3. 3.

    N. C. Jain and M. B. Marcus, “Sufficient conditions for the continuity of stationary Gaussian processes and applications to random functions,” Ann. Inst. Fourier,24, No. 2, 117–141 (1974).

  4. 4.

    A. Zygmund, Trigonometric Series, Vol. 1, Cambridge Univ. Press, Cambridge (1959).

  5. 5.

    I. A. Ibragimov, “Properties of realizations of random processes and embedding theorems,” Teor. Veroyatn. Ee Primen.,18, No. 3, 468–480 (1973).

  6. 6.

    N. N. Chentsov, “Weak convergence of random processes with trajectories without discontinuities of the second kind and the so-called ‘heuristic’ approach to goodness-of-fit tests of the Kolmogorov-Smirnov type,” Teor. Veroyatn. Ee Primen.,1, No. 1, 155–161 (1956).

  7. 7.

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

  8. 8.

    H. Gramer and M. Leadbetter, Stationary and Related Stochastic Processes, Wiley, New York (1967).

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 30, No. 2, pp. 241–247, March–April, 1978.

In conclusion, I express deep gratitude to M. I. Yadrenko for guidance in the preparation of this article.

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Matsak, I.K. Regularity of sampling distribution functions of a random process. Ukr Math J 30, 186–190 (1978). https://doi.org/10.1007/BF01085643

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Keywords

  • Distribution Function
  • Random Process
  • Sampling Distribution
  • Sampling Distribution Function