Stability of stochastic functional differential equations and the W-transform

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dc.contributor.authorKadiev, Ramazan
dc.contributor.authorPonosov, Arcady
dc.date.accessioned2021-04-26T18:19:51Z
dc.date.available2021-04-26T18:19:51Z
dc.date.issued2004-07-27
dc.description.abstractThe paper contains a systematic presentation of how the so-called "W-transform'' can be used to study stability of stochastic functional differential equations. The W-transform is an integral transform which typically is generated by a simpler differential equation ("reference equation'') via the Cauchy representation of its solutions ("variation-of-constant formula''). This other equation is supposed to have prescribed asymptotic properties (in this paper: Various kinds of stability). Applying the W-transform to the given equation produces an operator equation in a suitable space of stochastic processes, which depends on the asymptotic property we are interested in. In the paper we justify this method, describe some of its general properties, and illustrate the results by a number of examples.
dc.description.departmentMathematics
dc.formatText
dc.format.extent36 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationKadiev, R., & Ponosov, A. (2004). Stability of stochastic functional differential equations and the W-transform. <i>Electronic Journal of Differential Equations, 2004</i>(92), pp. 1-36.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/13446
dc.language.isoen
dc.publisherSouthwest Texas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.holderThis work is licensed under a Creative Commons Attribution 4.0 International License.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2004, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectStability
dc.subjectStochastic differential equations with aftereffect
dc.subjectIntegral transforms
dc.titleStability of stochastic functional differential equations and the W-transform
dc.typeArticle

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