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

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