Stability with probability I for solutions of linear stochastic differential-difference Ito’s equations
Conditions for absolute (independent of lags) asymptotic stability with probability 1 of systems of stochastic equations cited in the title of this paper are obtained. The proposed approach allows us to reduce the problem of analyzing stability to determination of the conditions for the existence of...
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| Date: | 2025 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian |
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Institute of Mathematics, NAS of Ukraine
2025
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/9347 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513502548983808 |
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| author | Zelentsovsky , A. L. Зеленцовский , A. Л. |
| author_facet | Zelentsovsky , A. L. Зеленцовский , A. Л. |
| author_sort | Zelentsovsky , A. L. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-06-30T14:20:55Z |
| description | Conditions for absolute (independent of lags) asymptotic stability with probability 1 of systems of stochastic equations cited in the title of this paper are obtained. The proposed approach allows us to reduce the problem of analyzing stability to determination of the conditions for the existence of a positively determined solution of a linear matrix equation. These conditions are stated in terms of locations of eigenvalues of the matrix constructed from the elements of the matrices of the initial system. |
| first_indexed | 2026-03-24T03:45:42Z |
| format | Article |
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| id | umjimathkievua-article-9347 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:45:42Z |
| publishDate | 2025 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/61/e8cfa51e5f36083c5f5dd6f987ec2a61.pdf |
| spelling | umjimathkievua-article-93472025-06-30T14:20:55Z Stability with probability I for solutions of linear stochastic differential-difference Ito’s equations Устойчивость с вероятностью I решений систем линейных стохастических дифференциально-разностных уравнений Ито Zelentsovsky , A. L. Зеленцовский , A. Л. - Conditions for absolute (independent of lags) asymptotic stability with probability 1 of systems of stochastic equations cited in the title of this paper are obtained. The proposed approach allows us to reduce the problem of analyzing stability to determination of the conditions for the existence of a positively determined solution of a linear matrix equation. These conditions are stated in terms of locations of eigenvalues of the matrix constructed from the elements of the matrices of the initial system. Получены условия абсолютной (не зависящей от запаздывания) асимптотической устойчивости с вероятностью 1 указанных в заглавии систем стохастических уравнений. Предлагаемый подход позволяет свести задачу анализа устойчивости к выяснению условий существования положительно определенного решения линейного матричного уравнения. Эти условия сформулированы в терминах расположения собственных значений матрицы, составленной из элементов матриц исходной системы. Отримано умови абсолютної (незалежної від запізнювань) асимптотичної стійкості з ймовірністю І вказаних в заголовку систем стохастичних рівнянь. Запропонований підхід дозволяє звести задачу аналізу стійкості до визначення умов існування додатньо означеного розв’язку лінійного матричного рівняння. Ці умови сформульовані в термінах розташування власних значень матриці, складеної з елементів матриць початкової системи. Institute of Mathematics, NAS of Ukraine 2025-06-30 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/9347 Ukrains’kyi Matematychnyi Zhurnal; Vol. 43 No. 2 (1991); 147-151 Український математичний журнал; Том 43 № 2 (1991); 147-151 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/9347/10497 Copyright (c) 1991 A. Л. Зеленцовский |
| spellingShingle | Zelentsovsky , A. L. Зеленцовский , A. Л. Stability with probability I for solutions of linear stochastic differential-difference Ito’s equations |
| title | Stability with probability I for solutions of linear stochastic differential-difference Ito’s equations |
| title_alt | Устойчивость с вероятностью I решений систем линейных стохастических дифференциально-разностных уравнений Ито |
| title_full | Stability with probability I for solutions of linear stochastic differential-difference Ito’s equations |
| title_fullStr | Stability with probability I for solutions of linear stochastic differential-difference Ito’s equations |
| title_full_unstemmed | Stability with probability I for solutions of linear stochastic differential-difference Ito’s equations |
| title_short | Stability with probability I for solutions of linear stochastic differential-difference Ito’s equations |
| title_sort | stability with probability i for solutions of linear stochastic differential-difference ito’s equations |
| topic_facet | - |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9347 |
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