Stability of the zero solution of nonlinear differential equations under the influence of white noise

Stabilita nulového řešení nelineárních diferenciálních rovnic pod vlivem bílého šumu

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Date
2015-05-07
Auteur
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10.1186/s13662-015-0482-y
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Résumé
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.
 
Článek zkoumá stabilitu nulového řešení nelineárních diferenciálních rovnic pod vlivem bílého šumu.
 
Keywords
stochastické systémy, bílý šum, mean square stability, Lyapunovova funkce, stochastic systems, white noise, mean square stability, Lyapunov function
URI
http://hdl.handle.net/11012/137371
Document type
Peer reviewed
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Source
Advances in Difference Equations. 2015, vol. 2015, issue 143, p. 0-0.
http://www.advancesindifferenceequations.com/content/2015/1/143
DOI
10.1186/s13662-015-0482-y
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