Asymptotic normality of spherical means of nonlinear functionals of Gaussian random fields
The central limit theorem is proved for the integral-type functionals of nonlinear transformations of two-and three-dimensional uniform isotropic Gaussian random fields. A theorem on convergence of finite-dimensional distributions of these functionals to the corresponding distributions of the Wiener...
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| Date: | 1993 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1993
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5834 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512055473209344 |
|---|---|
| author | Deriev, I. I. Дериев, И. И. Дериев, И. И. |
| author_facet | Deriev, I. I. Дериев, И. И. Дериев, И. И. |
| author_sort | Deriev, I. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:18:55Z |
| description | The central limit theorem is proved for the integral-type functionals of nonlinear transformations of two-and three-dimensional uniform isotropic Gaussian random fields. A theorem on convergence of finite-dimensional distributions of these functionals to the corresponding distributions of the Wiener process is also established. |
| first_indexed | 2026-03-24T03:22:42Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5834 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:22:42Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/42/7ebf90b75d2485f12c110ba9d4864242.pdf |
| spelling | umjimathkievua-article-58342020-03-19T09:18:55Z Asymptotic normality of spherical means of nonlinear functionals of Gaussian random fields Асимптотическая нормальность сферических средних нелинейных функционалов от гауссовских случайных полей Deriev, I. I. Дериев, И. И. Дериев, И. И. The central limit theorem is proved for the integral-type functionals of nonlinear transformations of two-and three-dimensional uniform isotropic Gaussian random fields. A theorem on convergence of finite-dimensional distributions of these functionals to the corresponding distributions of the Wiener process is also established. Доказаны центральная предельная теорема для функционалов интегрального типа от нелинейных преобразований гауссовских дву- и трехмерных однородных изотропных случайных полей и теорема о сходимости конечномерных распределений этих функционалов к соответствующим распределениям винеровского процесса. Institute of Mathematics, NAS of Ukraine 1993-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5834 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 4 (1993); 472–480 Український математичний журнал; Том 45 № 4 (1993); 472–480 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5834/8351 https://umj.imath.kiev.ua/index.php/umj/article/view/5834/8352 Copyright (c) 1993 Deriev I. I. |
| spellingShingle | Deriev, I. I. Дериев, И. И. Дериев, И. И. Asymptotic normality of spherical means of nonlinear functionals of Gaussian random fields |
| title | Asymptotic normality of spherical means of nonlinear functionals of Gaussian random fields |
| title_alt | Асимптотическая нормальность сферических средних нелинейных функционалов от гауссовских случайных полей |
| title_full | Asymptotic normality of spherical means of nonlinear functionals of Gaussian random fields |
| title_fullStr | Asymptotic normality of spherical means of nonlinear functionals of Gaussian random fields |
| title_full_unstemmed | Asymptotic normality of spherical means of nonlinear functionals of Gaussian random fields |
| title_short | Asymptotic normality of spherical means of nonlinear functionals of Gaussian random fields |
| title_sort | asymptotic normality of spherical means of nonlinear functionals of gaussian random fields |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5834 |
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