Estimation of an Unknown Parameter in the Cauchy Problem for a First-Order Partial Differential Equation under Small Gaussian Perturbations
On the basis of observation of a realization of a solution of the Cauchy problem, we establish a maximum-likelihood estimate for an unknown parameter. We construct an exponential inequality for the probabilities of large deviations of the estimate from the real value of the parameter.
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| Date: | 2000 |
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| Main Authors: | , , , , , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
2000
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4502 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510629324914688 |
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| author | Bondarev, B. V. Dzundza, A. I. Simogin, A. A. Бондарев, Б. В. Дзундза, А. И. Симогин, А. А. Бондарев, Б. В. Дзундза, А. И. Симогин, А. А. |
| author_facet | Bondarev, B. V. Dzundza, A. I. Simogin, A. A. Бондарев, Б. В. Дзундза, А. И. Симогин, А. А. Бондарев, Б. В. Дзундза, А. И. Симогин, А. А. |
| author_sort | Bondarev, B. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:30:08Z |
| description | On the basis of observation of a realization of a solution of the Cauchy problem, we establish a maximum-likelihood estimate for an unknown parameter. We construct an exponential inequality for the probabilities of large deviations of the estimate from the real value of the parameter. |
| first_indexed | 2026-03-24T03:00:02Z |
| format | Article |
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| id | umjimathkievua-article-4502 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:00:02Z |
| publishDate | 2000 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/e1/25cd538758c68fa469c6cccd13dd89e1.pdf |
| spelling | umjimathkievua-article-45022020-03-18T20:30:08Z Estimation of an Unknown Parameter in the Cauchy Problem for a First-Order Partial Differential Equation under Small Gaussian Perturbations Оценка неизвестного параметра в задаче Коши для уравнения в частных производных первого порядка при малых гауссовских возмущениях Bondarev, B. V. Dzundza, A. I. Simogin, A. A. Бондарев, Б. В. Дзундза, А. И. Симогин, А. А. Бондарев, Б. В. Дзундза, А. И. Симогин, А. А. On the basis of observation of a realization of a solution of the Cauchy problem, we establish a maximum-likelihood estimate for an unknown parameter. We construct an exponential inequality for the probabilities of large deviations of the estimate from the real value of the parameter. При спостереженні за реалізацією розв'язку задачі Коші отримано оцінку максимальної правдоподібності невідомого параметра. Побудовано експоненціальну нерівність для ймовірності великих відхилень оцінки від дійсного значення параметра. Institute of Mathematics, NAS of Ukraine 2000-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4502 Ukrains’kyi Matematychnyi Zhurnal; Vol. 52 No. 7 (2000); 999-1006 Український математичний журнал; Том 52 № 7 (2000); 999-1006 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4502/5708 https://umj.imath.kiev.ua/index.php/umj/article/view/4502/5709 Copyright (c) 2000 Bondarev B. V.; Dzundza A. I.; Simogin A. A. |
| spellingShingle | Bondarev, B. V. Dzundza, A. I. Simogin, A. A. Бондарев, Б. В. Дзундза, А. И. Симогин, А. А. Бондарев, Б. В. Дзундза, А. И. Симогин, А. А. Estimation of an Unknown Parameter in the Cauchy Problem for a First-Order Partial Differential Equation under Small Gaussian Perturbations |
| title | Estimation of an Unknown Parameter in the Cauchy Problem for a First-Order Partial Differential Equation under Small Gaussian Perturbations |
| title_alt | Оценка неизвестного параметра в задаче
Коши для уравнения в частных производных первого порядка при малых гауссовских возмущениях |
| title_full | Estimation of an Unknown Parameter in the Cauchy Problem for a First-Order Partial Differential Equation under Small Gaussian Perturbations |
| title_fullStr | Estimation of an Unknown Parameter in the Cauchy Problem for a First-Order Partial Differential Equation under Small Gaussian Perturbations |
| title_full_unstemmed | Estimation of an Unknown Parameter in the Cauchy Problem for a First-Order Partial Differential Equation under Small Gaussian Perturbations |
| title_short | Estimation of an Unknown Parameter in the Cauchy Problem for a First-Order Partial Differential Equation under Small Gaussian Perturbations |
| title_sort | estimation of an unknown parameter in the cauchy problem for a first-order partial differential equation under small gaussian perturbations |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4502 |
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