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dc.contributor.authorMargulies, William ( )
dc.contributor.authorZes, Dean ( )
dc.date.accessioned2021-05-14T20:31:06Z
dc.date.available2021-05-14T20:31:06Z
dc.date.issued2004-11-23
dc.identifier.citationMargulies, W., & Zes, D. (2004). A stochastic control problem. Electronic Journal of Differential Equations, 2004(135), pp. 1-10.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/13556
dc.description.abstractIn this paper, we study a specific stochastic differential equation depending on a parameter and obtain a representation of its probability density function in terms of Jacobi Functions. The equation arose in a control problem with a quadratic performance criteria. The quadratic performance is used to eliminate the control in the standard Hamilton-Jacobi variational technique. The resulting stochastic differential equation has a noise amplitude which complicates the solution. We then solve Kolmogorov's partial differential equation for the probability density function by using Jacobi Functions. A particular value of the parameter makes the solution a Martingale and in this case we prove that the solution goes to zero almost surely as time tends to infinity.en_US
dc.formatText
dc.format.extent10 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University-San Marcos, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2004, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectStochastic differential equationsen_US
dc.subjectControl problemsen_US
dc.subjectJacobi functionsen_US
dc.titleA stochastic control problemen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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