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General decay stability of stochastic functional differential equations

dc.contributor.advisorJanković, Svetlana
dc.contributor.otherPetrović, Ljiljana
dc.contributor.otherJovanović, Miljana
dc.contributor.otherMilošević, Marija
dc.creatorPavlović-Rajković, Gorica A.
dc.date.accessioned2016-01-05T13:23:39Z
dc.date.available2016-01-05T13:23:39Z
dc.date.available2020-07-03T16:11:49Z
dc.date.issued2014-07-21
dc.identifier.urihttp://eteze.ni.ac.rs/application/showtheses?thesesId=1337
dc.identifier.urihttps://nardus.mpn.gov.rs/handle/123456789/3963
dc.identifier.urihttps://fedorani.ni.ac.rs/fedora/get/o:878/bdef:Content/download
dc.identifier.urihttp://vbs.rs/scripts/cobiss?command=DISPLAY&base=70052&RID=1024759017
dc.description.abstractIn this thesis, pth moment and almost sure stability on a general decay rate for several types of stochastic functional differential equations were studied. By applying Razumikhin method and Lyapunov method stability criteria were obtained. Having in mind that some types of stochastic differential equations are not exponentially stable, the information about the stability with respect to a certain lower decay rate is very important, which was the motive for research in this paper. Some future research could focus on application of Krasovskii-Lyapunov method for exploring the general decay stability of the already studied types of stochastic differential equations. In this way, we could get different stability and decay rate criteria with respect to those obtained in the thesis. The research based on the modified results of this thesis could be continued for studying stability of various classes of stochastic functional differential equations with respect to martingale and martingale measures. The research on pth moment and almost sure stability and pth moment instability on a general decay rate for stochastic functional differential equations with Markovian switching and delayed impulses could be extended to stochastic differential equations with random impulses and Markovian switching which more realistically describe processes impulsive in kind. Also, Razumikhin method and Lyapunov method could be applied in studying pth moment and almost sure stability on a general decay rate for hybrid impulsive stochastic differential equations with switching not defined by Markov chain law as well as stochastic neural networks. Moreover, these methods could be used for studying general decay stability of all the above mentioned types of impulsive stochastic differential equations with respect to martingale and martingale measures. Some future research could be based on the application of LMI theory results to studying pth moment and almost sure stability on a general decay rate of perturbed impulsive stochastic functional differential equations with Markovian switching and hybrid perturbed impulsive stochastic functional differential equations.en
dc.formatapplication/pdf
dc.languagesr
dc.publisherУниверзитет у Нишу, Природно-математички факултетsr
dc.rightsopenAccessen
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.sourceУниверзитет у Нишуsr
dc.subjectMatematikasr
dc.subjectStochastic processesen
dc.subjectGaussov beli šumsr
dc.subjectmetoda Razumikhinasr
dc.subjectLyapunova metodasr
dc.subjectBrownovo kretanje (Wienerov proces)sr
dc.subjectdifferential equationsen
dc.subjectstabilityen
dc.titleOpšti tip stabilnosti stohastičkih funkcionalnih diferencijalnih jednačinasr
dc.titleGeneral decay stability of stochastic functional differential equationsen
dc.typedoctoralThesisen
dc.rights.licenseBY-NC-ND
dcterms.abstractЈанковић, Светлана; Милошевић, Марија; Јовановић, Миљана; Петровић, Љиљана; Павловић-Рајковић, Горица A.; Општи тип стабилности стохастичких функционалних диференцијалних једначина; Општи тип стабилности стохастичких функционалних диференцијалних једначина;
dc.identifier.fulltexthttps://nardus.mpn.gov.rs/bitstream/id/54168/Disertacija.pdf
dc.identifier.fulltexthttp://nardus.mpn.gov.rs/bitstream/id/54168/Disertacija.pdf
dc.identifier.rcubhttps://hdl.handle.net/21.15107/rcub_nardus_3963


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