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

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dc.contributor.authorDzhalladova, Iradacs
dc.contributor.authorRůžičková, Miroslavacs
dc.contributor.authorŠtoudková Růžičková, Vieracs
dc.coverage.issue143cs
dc.coverage.volume2015cs
dc.date.issued2015-05-07cs
dc.description.abstractThe 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.en
dc.description.abstractThe 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.en
dc.formattextcs
dc.format.extent0-0cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationAdvances in Difference Equations. 2015, vol. 2015, issue 143, p. 0-0.en
dc.identifier.doi10.1186/s13662-015-0482-ycs
dc.identifier.issn1687-1847cs
dc.identifier.orcid0000-0001-5493-7630cs
dc.identifier.other114441cs
dc.identifier.scopus57209151586cs
dc.identifier.urihttp://hdl.handle.net/11012/137371
dc.language.isoencs
dc.publisherSpringerOpencs
dc.relation.ispartofAdvances in Difference Equationscs
dc.relation.urihttp://www.advancesindifferenceequations.com/content/2015/1/143cs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/1687-1847/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectstochastic systemsen
dc.subjectwhite noiseen
dc.subjectmean square stabilityen
dc.subjectLyapunov functionen
dc.subjectstochastic systems
dc.subjectwhite noise
dc.subjectmean square stability
dc.subjectLyapunov function
dc.titleStability of the zero solution of nonlinear differential equations under the influence of white noiseen
dc.title.alternativeStability of the zero solution of nonlinear differential equations under the influence of white noiseen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-114441en
sync.item.dbtypeVAVen
sync.item.insts2025.10.14 15:06:48en
sync.item.modts2025.10.14 10:12:59en
thesis.grantorVysoké učení technické v Brně. Fakulta strojního inženýrství. Ústav matematikycs
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