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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Main Authors: Gang Li, Ming Chen
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/890925
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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.
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publishDate 2014-01-01
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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