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