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Teor. Veroyatnost. i Primenen., 1972, Volume 17, Issue 1, Pages 153–160 (Mi tvp4213)  

This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

On Lévy–Baxter Theorems for Random Fields

T. V. Arak

Leningrad

Abstract: Let $\xi(t)=\xi(t_1,…,t_k)$ be a Gaussian random field. In this paper, some sufficient conditions for convergence of the sums
$$ \sum_{\alpha_1,…,\alpha_k=1}^{2^n}F_n(\Delta_{2^{-n}}\xi(2^{-n}\alpha)), \quad \alpha=(\alpha_1,…,\alpha_k), $$
to a constant are obtained, where $\Delta_{2^{-n}}\xi(t)$ is the $k$th increment of the sample function $\xi(t)$ defined by (1) and $F_n$ are Borel functions. The results are analogues to those contained in [1]–[6] and can be considered as some generalizations of the theorem due to Berman in [5].

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English version:
Theory of Probability and its Applications, 1972, 17:1, 153–159

Bibliographic databases:

Received: 03.04.1970

Citation: T. V. Arak, “On Lévy–Baxter Theorems for Random Fields”, Teor. Veroyatnost. i Primenen., 17:1 (1972), 153–160; Theory Probab. Appl., 17:1 (1972), 153–159

Citation in format AMSBIB
\Bibitem{Ara72}
\by T.~V.~Arak
\paper On L\'evy--Baxter Theorems for Random Fields
\jour Teor. Veroyatnost. i Primenen.
\yr 1972
\vol 17
\issue 1
\pages 153--160
\mathnet{http://mi.mathnet.ru/tvp4213}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=298749}
\zmath{https://zbmath.org/?q=an:0301.60031}
\transl
\jour Theory Probab. Appl.
\yr 1972
\vol 17
\issue 1
\pages 153--159
\crossref{https://doi.org/10.1137/1117014}


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    This publication is cited in the following articles:
    1. S. M. Krasnitskiy, O. O. Kurchenko, “Baxter type theorems for generalized random Gaussian processes”, Theory Stoch. Process., 21(37):1 (2016), 45–52  mathnet  mathscinet  zmath
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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