Decomposition and stability of linear systems with multiplicative noise
type: Item
instance of: scholarly article
title: Decomposition and stability of linear systems with multiplicative noise
zbMATH Open document ID: 0568.93069
DOI: 10.1016/0005-1098(84)90086-4
author: Kazuhiko Terashima
author: Hajime Akashi
published in: Automatica
publication date: 1984-01-01T00:00:00Z
review text: This paper deals with linear stochastic systems of the form \(dX=a(t)Axdt+\sum B_ ix\circ dW_ i\), where ''\(\circ ''\) denotes the symmetric stochastic integral. The explicit solvability of these equations depends on the structure of the Lie algebra generated by \(\{A,B_ 1,...,B_ m\}\), see the work of \textit{A. J. Krener} and \textit{C. Lobry} [Stochastics 4, 193-203 (1981; Zbl 0452.60069)] for a general treatment of these problems. Once an explicit solution is obtained, stability properties (such as pth-mean, pth-order stability) can be discussed. The stability criteria are applied to an abelian and a solvable example.
Mathematics Subject Classification ID: 93E15
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 17B05
Mathematics Subject Classification ID: 91A60
zbMATH DE Number: 3908308
zbMATH Keywords: linear stochastic systems
zbMATH Keywords: explicit solvability
zbMATH Keywords: Lie algebra
zbMATH Keywords: stability criteria
reviewed by: Wolfgang Kliemann
MaRDI profile type: Publication
full work available at URL: 0005-1098(84)90086-4
OpenAlex ID: W2040809630
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description: scientific article; zbMATH DE number 3908308