On asymptotic normality of estimates for correlation functions of stationary Gaussian processes in the space of continuous functions
We establish conditions of the weak convergence of the empirical correlogram of a stationary Gaussian process to some Gaussian process in the space of continuous functions. We prove that such a convergence holds for a broad class of stationary Gaussian processes with square integrable spectral densi...
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| Datum: | 1995 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1995
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5539 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511774280777728 |
|---|---|
| author | Buldygin, V. V. Zayats, V. V. Булдигін, В. В. Заяц, В. В. |
| author_facet | Buldygin, V. V. Zayats, V. V. Булдигін, В. В. Заяц, В. В. |
| author_sort | Buldygin, V. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:13:12Z |
| description | We establish conditions of the weak convergence of the empirical correlogram of a stationary Gaussian process to some Gaussian process in the space of continuous functions. We prove that such a convergence holds for a broad class of stationary Gaussian processes with square integrable spectral density. |
| first_indexed | 2026-03-24T03:18:14Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5539 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:18:14Z |
| publishDate | 1995 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/f3/82701472eda0e4e2a6f9cc778e34d9f3.pdf |
| spelling | umjimathkievua-article-55392020-03-19T09:13:12Z On asymptotic normality of estimates for correlation functions of stationary Gaussian processes in the space of continuous functions Об асимптотической нормальности оценок корреляционных функций стационарных гауссовских процессов в пространстве непрерывных функций Buldygin, V. V. Zayats, V. V. Булдигін, В. В. Заяц, В. В. We establish conditions of the weak convergence of the empirical correlogram of a stationary Gaussian process to some Gaussian process in the space of continuous functions. We prove that such a convergence holds for a broad class of stationary Gaussian processes with square integrable spectral density. Розглянуто умови слабкої збіжності емпіричної корелограми стаціонарного гауссова процесу до деякого гауссова процесу в просторі неперервних функцій. Встановлено, що для широкого класу стаціонарних гауссових процесів з інтегровною у квадраті спектральною щільністю така збіжність має місце. Institute of Mathematics, NAS of Ukraine 1995-11-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5539 Ukrains’kyi Matematychnyi Zhurnal; Vol. 47 No. 11 (1995); 1485–1497 Український математичний журнал; Том 47 № 11 (1995); 1485–1497 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5539/7766 https://umj.imath.kiev.ua/index.php/umj/article/view/5539/7767 Copyright (c) 1995 Buldygin V. V.; Zayats V. V. |
| spellingShingle | Buldygin, V. V. Zayats, V. V. Булдигін, В. В. Заяц, В. В. On asymptotic normality of estimates for correlation functions of stationary Gaussian processes in the space of continuous functions |
| title | On asymptotic normality of estimates for correlation functions of stationary Gaussian processes in the space of continuous functions |
| title_alt | Об асимптотической нормальности оценок корреляционных
функций стационарных гауссовских процессов в пространстве непрерывных
функций |
| title_full | On asymptotic normality of estimates for correlation functions of stationary Gaussian processes in the space of continuous functions |
| title_fullStr | On asymptotic normality of estimates for correlation functions of stationary Gaussian processes in the space of continuous functions |
| title_full_unstemmed | On asymptotic normality of estimates for correlation functions of stationary Gaussian processes in the space of continuous functions |
| title_short | On asymptotic normality of estimates for correlation functions of stationary Gaussian processes in the space of continuous functions |
| title_sort | on asymptotic normality of estimates for correlation functions of stationary gaussian processes in the space of continuous functions |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5539 |
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