Equations for second moments of solutions of a system of linear differential equations with random semi-Markov coefficients and random input
We derive equations that determine second moments of a random solution of a system of Itô linear differential equations with coefficients depending on a finite-valued random semi-Markov process. We obtain necessary and sufficient conditions for the asymptotic stability of solutions in the mean squar...
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| Date: | 1999 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1999
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4664 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510817092370432 |
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| author | Lapshin, A. L. Лапшин, А. Л. Лапшин, А. Л. |
| author_facet | Lapshin, A. L. Лапшин, А. Л. Лапшин, А. Л. |
| author_sort | Lapshin, A. L. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:11:00Z |
| description | We derive equations that determine second moments of a random solution of a system of Itô linear differential equations with coefficients depending on a finite-valued random semi-Markov process. We obtain necessary and sufficient conditions for the asymptotic stability of solutions in the mean square with the use of moment equations and Lyapunov stochastic functions. |
| first_indexed | 2026-03-24T03:03:01Z |
| format | Article |
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| id | umjimathkievua-article-4664 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:03:01Z |
| publishDate | 1999 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/34/e5a08ce5145263c390ebd18907d71f34.pdf |
| spelling | umjimathkievua-article-46642020-03-18T21:11:00Z Equations for second moments of solutions of a system of linear differential equations with random semi-Markov coefficients and random input Уравнения для вторых моментов решений системы линейных дифференциальных уравнений со случайными полумарковскими коэффициентами и случайным входом Lapshin, A. L. Лапшин, А. Л. Лапшин, А. Л. We derive equations that determine second moments of a random solution of a system of Itô linear differential equations with coefficients depending on a finite-valued random semi-Markov process. We obtain necessary and sufficient conditions for the asymptotic stability of solutions in the mean square with the use of moment equations and Lyapunov stochastic functions. Виведено рівняння, що визначають другі моменти випадкового розв'язку системи лінійних диференціальних рівнянь Іто з коефіцієнтами, залежними від скінченнозначного випадкового напівмарковського процесу. Одержано необхідні та достатні умови асимптотичної стійкості розв'язків у середньому квадратичному з допомогою моментних рівнянь і стохастичних функцій Ляпунова. Institute of Mathematics, NAS of Ukraine 1999-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4664 Ukrains’kyi Matematychnyi Zhurnal; Vol. 51 No. 6 (1999); 776–783 Український математичний журнал; Том 51 № 6 (1999); 776–783 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4664/6030 https://umj.imath.kiev.ua/index.php/umj/article/view/4664/6031 Copyright (c) 1999 Lapshin A. L. |
| spellingShingle | Lapshin, A. L. Лапшин, А. Л. Лапшин, А. Л. Equations for second moments of solutions of a system of linear differential equations with random semi-Markov coefficients and random input |
| title | Equations for second moments of solutions of a system of linear differential equations with random semi-Markov coefficients and random input |
| title_alt | Уравнения для вторых моментов решений системы линейных дифференциальных уравнений со случайными полумарковскими коэффициентами и
случайным входом |
| title_full | Equations for second moments of solutions of a system of linear differential equations with random semi-Markov coefficients and random input |
| title_fullStr | Equations for second moments of solutions of a system of linear differential equations with random semi-Markov coefficients and random input |
| title_full_unstemmed | Equations for second moments of solutions of a system of linear differential equations with random semi-Markov coefficients and random input |
| title_short | Equations for second moments of solutions of a system of linear differential equations with random semi-Markov coefficients and random input |
| title_sort | equations for second moments of solutions of a system of linear differential equations with random semi-markov coefficients and random input |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4664 |
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