Relationship between spectral and coefficient criteria of mean-square stability for systems of linear stochastic differential and difference equations
We establish the relationship (equivalence) between the spectral and algebraic (coefficient) criteria (the latter is represented in terms of the Sylvester matrix algebraic equation) of mean-square asymptotic stability for three classes of systems of linear equations with varying random perturbations...
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| Date: | 2000 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian 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/4411 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510541451100160 |
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| author | Korenevsky, D. G. Коренівський, Д. Г. |
| author_facet | Korenevsky, D. G. Коренівський, Д. Г. |
| author_sort | Korenevsky, D. G. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:28:32Z |
| description | We establish the relationship (equivalence) between the spectral and algebraic (coefficient) criteria (the latter is represented in terms of the Sylvester matrix algebraic equation) of mean-square asymptotic stability for three classes of systems of linear equations with varying random perturbations of coefficients, namely, the ltô differential stochastic equations, difference stochastic equations with discrete time, and difference stochastic equations with continuous time. |
| first_indexed | 2026-03-24T02:58:38Z |
| format | Article |
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| id | umjimathkievua-article-4411 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:58:38Z |
| publishDate | 2000 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/3e/d00b928343d11980679a62ffacbd0f3e.pdf |
| spelling | umjimathkievua-article-44112020-03-18T20:28:32Z Relationship between spectral and coefficient criteria of mean-square stability for systems of linear stochastic differential and difference equations Взаємозв'язок спектрального і коефіцієнтного критеріїв стійкості в середньому квадратичному для систем лінійних стохастичних диференціальних та різницевих рівнянь Korenevsky, D. G. Коренівський, Д. Г. We establish the relationship (equivalence) between the spectral and algebraic (coefficient) criteria (the latter is represented in terms of the Sylvester matrix algebraic equation) of mean-square asymptotic stability for three classes of systems of linear equations with varying random perturbations of coefficients, namely, the ltô differential stochastic equations, difference stochastic equations with discrete time, and difference stochastic equations with continuous time. Встановлено взаємозв'язок (еквівалентність) спектрального і алгебраїчного, коефіцієнтного (вираженого в термінах матричного алгебраїчного рівняння Сільвестра) критеріїв асимптотичної стійкості в середньому квадратичному для трьох класів систем лінійних рівнянь із змінними випадковими збуреннями коефіцієнтів - диференціальних стохастичних рівнянь Іто, різницевих стохастичних рівнянь з дискретним часом та різницевих стохастичних рівнянь з неперервним часом. Institute of Mathematics, NAS of Ukraine 2000-02-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4411 Ukrains’kyi Matematychnyi Zhurnal; Vol. 52 No. 2 (2000); 228-233 Український математичний журнал; Том 52 № 2 (2000); 228-233 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4411/5526 https://umj.imath.kiev.ua/index.php/umj/article/view/4411/5527 Copyright (c) 2000 Korenevsky D. G. |
| spellingShingle | Korenevsky, D. G. Коренівський, Д. Г. Relationship between spectral and coefficient criteria of mean-square stability for systems of linear stochastic differential and difference equations |
| title | Relationship between spectral and coefficient criteria of mean-square stability for systems of linear stochastic differential and difference equations |
| title_alt | Взаємозв'язок спектрального і коефіцієнтного критеріїв стійкості в середньому квадратичному для систем лінійних стохастичних диференціальних та різницевих рівнянь |
| title_full | Relationship between spectral and coefficient criteria of mean-square stability for systems of linear stochastic differential and difference equations |
| title_fullStr | Relationship between spectral and coefficient criteria of mean-square stability for systems of linear stochastic differential and difference equations |
| title_full_unstemmed | Relationship between spectral and coefficient criteria of mean-square stability for systems of linear stochastic differential and difference equations |
| title_short | Relationship between spectral and coefficient criteria of mean-square stability for systems of linear stochastic differential and difference equations |
| title_sort | relationship between spectral and coefficient criteria of mean-square stability for systems of linear stochastic differential and difference equations |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4411 |
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