دانلود مقاله : Strong solutions of a class of hybrid diffusion processes with state-dependent regim

چکیده : 

Thisworkfocusesonthestrongsolutionsofaclassofhybriddiffusionprocesseswithstate-dependentregime-switching.Thisimportantclassofprocessesoriginatesfromthepurposeofmodelingtheinterestrateinfinance.Theyhavenoanyexplicitsolutions.Moreover,state-dependentregime-switchingandnon-Lipschitzdiffusioncoefficientposeachallengetoouranalysis.Toovercomeallofthese,weconsidertheEulernumericalschemesratherthanthetraditionalPicarditerationsintheexistingresultsofsolutionsofstochasticdifferentialequations.Theweakconvergenceofnumericalalgorithmsisfirstestablishedbyamartingaleproblemformulation.Usingthisresult,wecanalsoobtainthestrongconvergenceofthealgorithms.Theexistenceofstrongsolutionsisthenconfirmed.Inaddition,decreasingstepsizeiterativealgorithmsandtheirweakconvergencearepresented.Severalnumericalexperimentsarealsoprovidedforillustration.