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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Published in | Ukrainian mathematical journal Vol. 58; no. 4; pp. 619 - 629 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
New York
Springer Nature B.V
01.04.2006
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Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 0041-5995 1573-9376 |
DOI: | 10.1007/s11253-006-0087-4 |