Investigation of exponential dichotomy of linear Itô stochastic systems with random initial data by using quadratic forms

We study conditions for the mean-square exponential dichotomy of linear Itô stochastic systems. We prove that a sufficient condition for exponential dichotomy is the existence of a quadratic form whose derivative along the solutions of a system is negative definite. The converse theorem is also prov...

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Bibliographic Details
Published inUkrainian mathematical journal Vol. 58; no. 4; pp. 619 - 629
Main Authors Stanzhyts’kyi, O. M., Krenevych, A. P.
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.04.2006
Subjects
Quadratic forms
Stochastic systems
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Summary:We study conditions for the mean-square exponential dichotomy of linear Itô stochastic systems. We prove that a sufficient condition for exponential dichotomy is the existence of a quadratic form whose derivative along the solutions of a system is negative definite. The converse theorem is also proved.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-006-0087-4