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On Baxter Type Theorems for Generalized Random Gaussian Processes with Independent Values

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Abstract

We construct suitable families of basic functions and prove theorems of Baxter type for generalized Gaussian random processes with independent values. These theorems are used to divide families of such processes into classes. The singularity of probability measures corresponding to representatives of different classes is proved.

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References

  1. I. M. Gelfand and G. E. Shilov, Generalized Functions and Operations over them [in Russian], Gos. Izd. Fiz.-Mat. Lit., Moscow (1959).

    Google Scholar 

  2. L. Hormander, The Analysis of Linear Partial Differential Operators, Springer-Verlag, Berlin–Heidelberg (2003).

    Book  Google Scholar 

  3. Yu. A. Rozanov, Random Fields and Stochastic Partial Differential Equations [in Russian], Nauka, Moscow (1995).

    Google Scholar 

  4. I. M. Gelfand and N. Ya. Vilenkin, Some Applications of the Fourier Analysis. Equipped Hilbert Spaces [in Russian], Gos. Izd. Fiz.-Mat. Lit., Moscow (1961).

    Google Scholar 

  5. Yu. V. Kozachenko, O. O. Kurchenko, and O. O. Sinyavs’ka, The Levi–Baxter Theorems for Random Fields and their Application [in Ukrainian], Autdor-Shark, Uzhgorod (2018).

    Google Scholar 

  6. P. Levy, “Le mouvement Brownian plan,” Amer. J. Math., Vol. 62, 487–550 (1940).

    Article  MathSciNet  Google Scholar 

  7. G. Baxter, “A strong limit theorem for Gaussian processes,” Proc. Amer. Math. Soc., Vol. 7, No. 3, 522–527 (1956).

    Article  MathSciNet  Google Scholar 

  8. V. B. Goryainov, “On the Levi–Baxter theorems for stochastic elliptical equations,” Teoriya Veroyatn. i yeyo Primeneniya, Vol. 33, Issue 1, 176–179 (1988).

    MathSciNet  MATH  Google Scholar 

  9. S. M. Krasnitskiy and O. O. Kurchenko, “Baxter type theorems for generalized random Gaussian processes,” Theory of Stoch. Proc., Vol. 21(37), No. 1, 45–52 (2016).

  10. S. Krasnitskiy and O. Kurchenko, “On Baxter type theorems for generalized random Gaussian fields,” in: Stochastic Processes and Applications, SPAS 2017, S. Silvestrov, A. Malyarenko, and M. Rancic (eds.), Springer Proc. in Mathematics & Statistics, Vol. 271, Springer, Cham (2018), pp. 91–103. https://doi.org/https://doi.org/10.1007/978-3-030-02825-1_4.

  11. S. M. Krasnitskii, “Necessary and sufficient conditions of equivalence of probability measures corresponding to homogeneous random fields with spectral density,” Cybern. Syst. Analysis, Vol. 33, No. 5, 641–646 (1997).

    Article  Google Scholar 

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Authors and Affiliations

  1. Kyiv National University of Technologies and Design, Kyiv, Ukraine

    S. M. Krasnitskiy

  2. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    O. O. Kurchenko

Authors
  1. S. M. Krasnitskiy
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  2. O. O. Kurchenko
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Correspondence to S. M. Krasnitskiy.

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Translated from Kibernetika i Sistemnyi Analiz, No. 2, March–April, 2020, pp. 66–74.

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Krasnitskiy, S.M., Kurchenko, O.O. On Baxter Type Theorems for Generalized Random Gaussian Processes with Independent Values. Cybern Syst Anal 56, 223–230 (2020). https://doi.org/10.1007/s10559-020-00238-5

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  • DOI: https://doi.org/10.1007/s10559-020-00238-5

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