Stability of the zero solution of nonlinear differential equations under the influence of white noise
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Dzhalladova, Irada
Růžičková, Miroslava
Štoudková Růžičková, Viera
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Mark
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SpringerOpen
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0000-0001-5493-7630 Altmetrics
Abstract
The paper deals with a system of nonlinear differential equations under the influence of white noise. This system can be used as a mathematical model of various real problems in finance, mathematical biology, climatology, signal theory and others. Necessary and sufficient conditions for the asymptotic mean square stability of the zero solution of this system are derived in the paper. The paper introduces a new approach to studying such problems - construction of a suitable deterministic system with the use of Lyapunov function.
The paper deals with a system of nonlinear differential equations under the influence of white noise. This system can be used as a mathematical model of various real problems in finance, mathematical biology, climatology, signal theory and others. Necessary and sufficient conditions for the asymptotic mean square stability of the zero solution of this system are derived in the paper. The paper introduces a new approach to studying such problems - construction of a suitable deterministic system with the use of Lyapunov function.
The paper deals with a system of nonlinear differential equations under the influence of white noise. This system can be used as a mathematical model of various real problems in finance, mathematical biology, climatology, signal theory and others. Necessary and sufficient conditions for the asymptotic mean square stability of the zero solution of this system are derived in the paper. The paper introduces a new approach to studying such problems - construction of a suitable deterministic system with the use of Lyapunov function.
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Advances in Difference Equations. 2015, vol. 2015, issue 143, p. 0-0.
http://www.advancesindifferenceequations.com/content/2015/1/143
http://www.advancesindifferenceequations.com/content/2015/1/143
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Peer-reviewed
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en
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