Input-to-State Stability of Linear Stochastic Functional Differential Equations
The purpose of the paper is to show how asymptotic properties, first of all stochastic Lyapunov stability, of linear stochastic functional differential equations can be studied via the property of solvability of the equation in certain pairs of spaces of stochastic processes, the property which we c...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/8901563 |
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| _version_ | 1832548075869044736 |
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| author | Ramazan Kadiev Arcady Ponosov |
| author_facet | Ramazan Kadiev Arcady Ponosov |
| author_sort | Ramazan Kadiev |
| collection | DOAJ |
| description | The purpose of the paper is to show how asymptotic properties, first of all stochastic Lyapunov stability, of linear stochastic functional differential equations can be studied via the property of solvability of the equation in certain pairs of spaces of stochastic processes, the property which we call input-to-state stability with respect to these spaces. Input-to-state stability and hence the desired asymptotic properties can be effectively verified by means of a special regularization, also known as “the W-method” in the literature. How this framework provides verifiable conditions of different kinds of stochastic stability is shown. |
| format | Article |
| id | doaj-art-ab2f8dfded764bfab53c38dca3a7136c |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-ab2f8dfded764bfab53c38dca3a7136c2025-02-03T06:42:15ZengWileyJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/89015638901563Input-to-State Stability of Linear Stochastic Functional Differential EquationsRamazan Kadiev0Arcady Ponosov1Dagestan Research Center, The Russian Academy of Sciences and Department of Mathematics, Dagestan State University, Makhachkala 367005, RussiaDepartment of Mathematical Sciences and Technology, Norwegian University of Life Sciences, P.O. Box 5003, 1432 Ås, NorwayThe purpose of the paper is to show how asymptotic properties, first of all stochastic Lyapunov stability, of linear stochastic functional differential equations can be studied via the property of solvability of the equation in certain pairs of spaces of stochastic processes, the property which we call input-to-state stability with respect to these spaces. Input-to-state stability and hence the desired asymptotic properties can be effectively verified by means of a special regularization, also known as “the W-method” in the literature. How this framework provides verifiable conditions of different kinds of stochastic stability is shown.http://dx.doi.org/10.1155/2016/8901563 |
| spellingShingle | Ramazan Kadiev Arcady Ponosov Input-to-State Stability of Linear Stochastic Functional Differential Equations Journal of Function Spaces |
| title | Input-to-State Stability of Linear Stochastic Functional Differential Equations |
| title_full | Input-to-State Stability of Linear Stochastic Functional Differential Equations |
| title_fullStr | Input-to-State Stability of Linear Stochastic Functional Differential Equations |
| title_full_unstemmed | Input-to-State Stability of Linear Stochastic Functional Differential Equations |
| title_short | Input-to-State Stability of Linear Stochastic Functional Differential Equations |
| title_sort | input to state stability of linear stochastic functional differential equations |
| url | http://dx.doi.org/10.1155/2016/8901563 |
| work_keys_str_mv | AT ramazankadiev inputtostatestabilityoflinearstochasticfunctionaldifferentialequations AT arcadyponosov inputtostatestabilityoflinearstochasticfunctionaldifferentialequations |