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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 890925, 6 pages
http://dx.doi.org/10.1155/2014/890925
Research Article

On Uniqueness of Strong Solution of Stochastic Systems

School of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 265590, China

Received 25 October 2013; Revised 5 January 2014; Accepted 11 January 2014; Published 24 February 2014

Academic Editor: Antonio Suárez

Copyright © 2014 Gang Li and Ming Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.