The required ansatz to construct Lie point transformations and the symmetries of a first-order stochastic differential equation

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dc.contributor.advisorFredericks, Ebrahimen_ZA
dc.contributor.advisorEbobisse Bille, Francoisen_ZA
dc.contributor.authorMasike, Kakanyo Knowledgeen_ZA
dc.date.accessioned2015-10-06T14:15:37Z
dc.date.available2015-10-06T14:15:37Z
dc.date.issued2011en_ZA
dc.description.abstractIn this thesis we demonstrate how to obtain the required ansatz to determine Lie point transformations of evolution-type equations from the contact transformation approach. We indicate that the Lie point transformations of the Fokker-Planck equation (FPE), which is a second-order linear parabolic partial differential equation (PDE), are projectable by using the ansatz. We further obtain the symmetries of a stochastic ordinary differential equation (SODE) which corresponds to those of the FPE. This is possible because there exists a relationship between an SODE and the associated (deterministic) FPE. The study of SODEs is an interesting and applicable concept in the real world and one of the building factors to this study is an Ito integral. These Ito integrals are of much use, for instance, in the field of mathematical finance whereby its use has shown the relationship between call options and their non-deterministic underlying stock prices. Wiener processes must be considered in finding an approximation of these integrals. Acclimatization of Sophus Lie's work to SODEs has been done by (Gaeta and Quintero [2]; Wafo Soh and Mahomed [41]; Unal [42]; Fredericks and Mahomed [43]). The determining equations for the first-order SODEs are derived in an Ito calculus context and are non-stochastic. Consequently, symmetries of an SODE are obtained without the consultation of its corresponding FPE.en_ZA
dc.identifier.apacitationMasike, K. K. (2011). <i>The required ansatz to construct Lie point transformations and the symmetries of a first-order stochastic differential equation</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/14145en_ZA
dc.identifier.chicagocitationMasike, Kakanyo Knowledge. <i>"The required ansatz to construct Lie point transformations and the symmetries of a first-order stochastic differential equation."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2011. http://hdl.handle.net/11427/14145en_ZA
dc.identifier.citationMasike, K. 2011. The required ansatz to construct Lie point transformations and the symmetries of a first-order stochastic differential equation. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Masike, Kakanyo Knowledge AB - In this thesis we demonstrate how to obtain the required ansatz to determine Lie point transformations of evolution-type equations from the contact transformation approach. We indicate that the Lie point transformations of the Fokker-Planck equation (FPE), which is a second-order linear parabolic partial differential equation (PDE), are projectable by using the ansatz. We further obtain the symmetries of a stochastic ordinary differential equation (SODE) which corresponds to those of the FPE. This is possible because there exists a relationship between an SODE and the associated (deterministic) FPE. The study of SODEs is an interesting and applicable concept in the real world and one of the building factors to this study is an Ito integral. These Ito integrals are of much use, for instance, in the field of mathematical finance whereby its use has shown the relationship between call options and their non-deterministic underlying stock prices. Wiener processes must be considered in finding an approximation of these integrals. Acclimatization of Sophus Lie's work to SODEs has been done by (Gaeta and Quintero [2]; Wafo Soh and Mahomed [41]; Unal [42]; Fredericks and Mahomed [43]). The determining equations for the first-order SODEs are derived in an Ito calculus context and are non-stochastic. Consequently, symmetries of an SODE are obtained without the consultation of its corresponding FPE. DA - 2011 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2011 T1 - The required ansatz to construct Lie point transformations and the symmetries of a first-order stochastic differential equation TI - The required ansatz to construct Lie point transformations and the symmetries of a first-order stochastic differential equation UR - http://hdl.handle.net/11427/14145 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/14145
dc.identifier.vancouvercitationMasike KK. The required ansatz to construct Lie point transformations and the symmetries of a first-order stochastic differential equation. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2011 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/14145en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematics and Applied Mathematicsen_ZA
dc.titleThe required ansatz to construct Lie point transformations and the symmetries of a first-order stochastic differential equationen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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