Approximation of some discrete-time stochastic processes by diﬀerential equations

Thisworkdealswithsolutionsofordinarydiﬀerentialequationsasapproximationsofsomediscrete-timestochasticprocesses.Similarly,thesestochasticprocessesmaybeseenasschemesofapproximationforthissolution.Indeed,thesestochasticschemesaredeﬁnedandtheirconvergencetothesolutionofadiﬀerentialequationisproven.More-over,theasymptoticdistributionoftheﬂuctuationsaboutthelimitsolutionisstudied.Thisfactgivestheasymptoticdistributionofarandomglobalerrorofapproximation.MainresultsareillustratedbymeansofthesocalledSISepidemicmodelandnumericalsimulationsarecarriedout.

PDF

___

[1]S.Abbasbandy,C.Bervillier,Analyticcontinuationoftaylorseriesandtheboundaryvalue problemsofsomenonlinearordinarydiﬀerentialequations,AppliedMathematicsandCom- putationvol.218(no.5)(2011)21782199.
[2]P.Billingsley,ConvergenceofProbabilityMeasures,Wiley&Sons,NewYork,1968. [3]R.W.RDarling,J.R.Norris,DiﬀerentialequationapproximationsforMarkovChain,Prob- abilitySurveysVol.5(2008)37-79.
[4]M.D.M.R.Eslahchi,S.Ahmadi-Asl,Thegeneraljacobimatrixmethodforsolvingsome nonlinearordinarydiﬀerentialequations,AppliedMathematicalModelling(InPress)(2012) 19.
[5]S.K.K.Parand,S.Abbasbandy,J.Rad,Anovelapplicationofradialbasisfunctions forsolvingamodelofﬁrst-orderintegro-ordinarydiﬀerentialequation,Communicationsin NonlinearScienceandNumericalSimulationVol.16(No.11)(2012)42504258. [6]R.Fierro,S.Torres,Astochasticschemeofapproximationforordinarydiﬀerentialequations, ElectronicCommunicationsinProbabilityVol.13(2008)19. [7]R.Fierro,Aclassofstochasticepidemicmodelsanditsdeterministiccounterpart,Journal oftheKoreanStatisticalSocietyVol.39(No.4)(2010)397407. [8]P.Kloeden,E.Platen,NumericalSolutionofStochasticDiﬀerentialEquations,Springer, NewYork,1995.
[9]T.G.Kurtz,SolutionsofordinarydiﬀerentialequationsaslimitsofpurejumpMarkov processes,JournalofAppliedProbability,Vol.7(No.1)(1970)49-58. [10]T.G.Kurtz,LimittheoremsforsequencesofjumpMarkovprocessesapproximatingordinary diﬀerentialprocesses,JournalofAppliedProbability,Vol.8(No.2)(1971)344-356.
[11]T.G.Kurtz,ApproximationofPopulationProcesses,SeriesinAppliedMathematics36. Philadelphia:SIAM,1981.
[12]H.Kushner,P.Dupuis,NumericalMethodsforStochasticControlProblemsinContinuous Time,Springer,NewYork,1991.
[13]E.Lenglart,Relationdedominationentredeuxprocessus,AnnalesdelInstitutHenri Poincaré(B)ProbabilitésetStatistiquesVol.13(No.2)(1977)171179.
[14]R.Rebolledo,Laméthodedesmartingalesappliquéeáletudedelaconvergenceenloide processus,MémoiresdelaSociétéMathématiquedeFranceVol.62(No.4)(1979)1125.

Hacettepe Journal of Mathematics and Statistics-Cover

Yayın Aralığı: Yılda 6 Sayı
Başlangıç: 2002
Yayıncı: Hacettepe Üniversitesi Fen Fakultesi

Arşiv