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Numerical treatment of stochastic differential equations: Diffusion and jump-diffusion processes with applications

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dc.contributor.author Boukhelkhal, Ikram
dc.date.accessioned 2024-06-23T09:51:58Z
dc.date.available 2024-06-23T09:51:58Z
dc.date.issued 2024-06-13
dc.identifier.issn MD/23
dc.identifier.uri https://dspace.univ-bba.dz:443/xmlui/handle/123456789/5035
dc.description.abstract In thisdissertation,wedealwiththeproblemofsimulatingstochasticdifferentialequations driven byBrownianmotionorthegeneralL´evy processes.First,weestablishthebasic theory ofstochasticcalculusandintroducetheIt ˆo-Taylorexpansionforstochasticdifferen- tial equations(SDEs).Inaddition,wepresentvariousnumericalschemesderivedfrom the It ˆo-Taylorexpansion.ThesemethodsareusedtosolvethestochasticLorenzequa- tion, thestochasticDuffingequation,andtheMertonmodelequation.Inaddition,spec- tral techniquesareadaptedforthenumericalsolutionofnonlinearstochasticdifferential equations. Further,generalizedLagrangeinterpolationfunctionsareproposedforsolving various typesofSDEs,offeringsignificantperformanceimprovements. en_US
dc.language.iso en en_US
dc.publisher UNIVERSITY BBA en_US
dc.subject Stochastic differentialequation,Brownianmotion,jumpdiffusion,spectral method, numericalsolution,collocationmethod. i en_US
dc.title Numerical treatment of stochastic differential equations: Diffusion and jump-diffusion processes with applications en_US
dc.type Thesis en_US


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