On uniqueness of strong solution of stochastic systems
type: Item
instance of: scholarly article
title: On uniqueness of strong solution of stochastic systems
zbMATH Open document ID: 1406.93369
DOI: 10.1155/2014/890925
author: Gang Li
author: Ming Chen
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: 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 [\textit{W. Zhang} et al., IEEE Trans. Autom. Control 53, No. 7, 1630--1642 (2008; Zbl 1367.93549)] 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.
Mathematics Subject Classification ID: 93E15
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 7023247
zbMATH Keywords: stochastic linear systems
zbMATH Keywords: matrix Riccati equations
zbMATH Keywords: mean square stabilization
Wikidata QID: Q59042269
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/890925
OpenAlex ID: W2002995175
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description: scientific article; zbMATH DE number 7023247