Exponential stability of linear stochastic differential equations with bounded delay and the W-transform
We demonstrate how the method of auxiliary ('reference') equations, also known as N. V. Azbelev's W-transform method, can be used to derive efficient conditions for the exponential Lyapunov stability of linear delay equations driven by a vector-valued Wiener process. For the sake of c...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2008-07-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=337 |
| _version_ | 1797830798878965760 |
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| author | R. I. Kadiev Arkadi Ponosov |
| author_facet | R. I. Kadiev Arkadi Ponosov |
| author_sort | R. I. Kadiev |
| collection | DOAJ |
| description | We demonstrate how the method of auxiliary ('reference') equations, also known as N. V. Azbelev's W-transform method, can be used to derive efficient conditions for the exponential Lyapunov stability of linear delay equations driven by a vector-valued Wiener process. For the sake of convenience the W-method is briefly outlined in the paper, its justification is however omitted. The paper contains a general stability result, which is specified in the last section in the form of seven corollaries providing sufficient stability conditions for some important classes of It\^{o} equations with delay. |
| first_indexed | 2024-04-09T13:41:54Z |
| format | Article |
| id | doaj.art-a714fba0228e4a36ac57c771ba34e273 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:41:54Z |
| publishDate | 2008-07-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-a714fba0228e4a36ac57c771ba34e2732023-05-09T07:52:58ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752008-07-0120082311410.14232/ejqtde.2008.1.23337Exponential stability of linear stochastic differential equations with bounded delay and the W-transformR. I. Kadiev0Arkadi Ponosov1Dagestan Scientific Center, Russian Academy of Sciences, Makhachkala, RussiaNorwegian University of Life Sciences, As, NorwayWe demonstrate how the method of auxiliary ('reference') equations, also known as N. V. Azbelev's W-transform method, can be used to derive efficient conditions for the exponential Lyapunov stability of linear delay equations driven by a vector-valued Wiener process. For the sake of convenience the W-method is briefly outlined in the paper, its justification is however omitted. The paper contains a general stability result, which is specified in the last section in the form of seven corollaries providing sufficient stability conditions for some important classes of It\^{o} equations with delay.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=337 |
| spellingShingle | R. I. Kadiev Arkadi Ponosov Exponential stability of linear stochastic differential equations with bounded delay and the W-transform Electronic Journal of Qualitative Theory of Differential Equations |
| title | Exponential stability of linear stochastic differential equations with bounded delay and the W-transform |
| title_full | Exponential stability of linear stochastic differential equations with bounded delay and the W-transform |
| title_fullStr | Exponential stability of linear stochastic differential equations with bounded delay and the W-transform |
| title_full_unstemmed | Exponential stability of linear stochastic differential equations with bounded delay and the W-transform |
| title_short | Exponential stability of linear stochastic differential equations with bounded delay and the W-transform |
| title_sort | exponential stability of linear stochastic differential equations with bounded delay and the w transform |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=337 |
| work_keys_str_mv | AT rikadiev exponentialstabilityoflinearstochasticdifferentialequationswithboundeddelayandthewtransform AT arkadiponosov exponentialstabilityoflinearstochasticdifferentialequationswithboundeddelayandthewtransform |