On Uniqueness of Strong Solution of Stochastic Systems
A kind of the well-known matrix Riccati equations which arise in certain stochastic optimal problems is investigated. With the aid of the operator spectrum and the generalized Lyapunov equation approach, we give a sufficient condition for existence and uniqueness of the strong solution related to th...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/890925 |
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| _version_ | 1849434721344290816 |
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| author | Gang Li Ming Chen |
| author_facet | Gang Li Ming Chen |
| author_sort | Gang Li |
| collection | DOAJ |
| description | A kind of the well-known matrix Riccati equations which arise in certain stochastic optimal problems is investigated. With the aid of the operator spectrum and the generalized Lyapunov equation approach, we give a sufficient condition for existence and uniqueness of the strong solution related to
the critical mean square stabilization of stochastic linear controlled systems, which proves Conjecture 10 in (Zhang et al. (2008)) to a large extent. In addition, we get some properties of the strong solution. At last, we give a kind of stochastic system which has only a strong solution by an example. |
| format | Article |
| id | doaj-art-e3eb75a401814dc1b24408c663b64c20 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e3eb75a401814dc1b24408c663b64c202025-08-20T03:26:33ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/890925890925On Uniqueness of Strong Solution of Stochastic SystemsGang Li0Ming Chen1School of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 265590, ChinaSchool of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 265590, ChinaA kind of the well-known matrix Riccati equations which arise in certain stochastic optimal problems is investigated. With the aid of the operator spectrum and the generalized Lyapunov equation approach, we give a sufficient condition for existence and uniqueness of the strong solution related to the critical mean square stabilization of stochastic linear controlled systems, which proves Conjecture 10 in (Zhang et al. (2008)) to a large extent. In addition, we get some properties of the strong solution. At last, we give a kind of stochastic system which has only a strong solution by an example.http://dx.doi.org/10.1155/2014/890925 |
| spellingShingle | Gang Li Ming Chen On Uniqueness of Strong Solution of Stochastic Systems Abstract and Applied Analysis |
| title | On Uniqueness of Strong Solution of Stochastic Systems |
| title_full | On Uniqueness of Strong Solution of Stochastic Systems |
| title_fullStr | On Uniqueness of Strong Solution of Stochastic Systems |
| title_full_unstemmed | On Uniqueness of Strong Solution of Stochastic Systems |
| title_short | On Uniqueness of Strong Solution of Stochastic Systems |
| title_sort | on uniqueness of strong solution of stochastic systems |
| url | http://dx.doi.org/10.1155/2014/890925 |
| work_keys_str_mv | AT gangli onuniquenessofstrongsolutionofstochasticsystems AT mingchen onuniquenessofstrongsolutionofstochasticsystems |