KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2014 / Cilt: 43 - Sayı: 6

Approximation of some discrete-time stochastic processes by differential equations

Raúl FİERRO
Sayfa
1035–1046
Yayın Tarihi
2022-10-18
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:Thisworkdealswithsolutionsofordinarydifferentialequationsasapproximationsofsomediscrete-timestochasticprocesses.Similarly,thesestochasticprocessesmaybeseenasschemesofapproximationforthissolution.Indeed,thesestochasticschemesaredefinedandtheirconvergencetothesolutionofadifferentialequationisproven.More-over,theasymptoticdistributionofthefluctuationsaboutthelimitsolutionisstudied.Thisfactgivestheasymptoticdistributionofarandomglobalerrorofapproximation.MainresultsareillustratedbymeansofthesocalledSISepidemicmodelandnumericalsimulationsarecarriedout.
📊
Temel Bulgular & Veri:Thisworkdealswithsolutionsofordinarydifferentialequationsasapproximationsofsomediscrete-timestochasticprocesses.Similarly,thesestochasticprocessesmaybeseenasschemesofapproximationforthissolution.Indeed,thesestochasticschemesaredefinedandtheirconvergencetothesolutionofadifferentialequationisproven.More-over,theasymptoticdistributionofthefluctuationsaboutthelimitsolutionisstudied.Thisfactgivestheasymptoticdistributionofarandomglobalerrorofapproximation.MainresultsareillustratedbymeansofthesocalledSISepidemicmodelandnumericalsimulationsarecarriedout.
💡
Sonuç & Katkı:Thisworkdealswithsolutionsofordinarydifferentialequationsasapproximationsofsomediscrete-timestochasticprocesses.Similarly,thesestochasticprocessesmaybeseenasschemesofapproximationforthissolution.Indeed,thesestochasticschemesaredefinedandtheirconvergencetothesolutionofadifferentialequationisproven.More-over,theasymptoticdistributionofthefluctuationsaboutthelimitsolutionisstudied.Thisfactgivestheasymptoticdistributionofarandomglobalerrorofapproximation.MainresultsareillustratedbymeansofthesocalledSISepidemicmodelandnumericalsimulationsarecarriedout.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

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

🔖

Bu Makaleye Atıf Yap

FİERRO, R. (2022). Approximation of some discrete-time stochastic processes by differential equations. Hacettepe Journal of Mathematics and Statistics, Cilt: 43 - Sayı: 6, 1035–1046. https://ajindex.com/articles/530311

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (1)

  1. S.Abbasbandy,C.Bervillier,Analyticcontinuationoftaylorseriesandtheboundaryvalue problemsofsomenonlinearordinarydifferentialequations,AppliedMathematicsandCom- putationvol.218(no.5)(2011)2178–2199. [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) 1–9. [5]S.K.K.Parand,S.Abbasbandy,J.Rad,Anovelapplicationofradialbasisfunctions forsolvingamodeloffirst-orderintegro-ordinarydifferentialequation,Communicationsin NonlinearScienceandNumericalSimulationVol.16(No.11)(2012)4250–4258. [6]R.Fierro,S.Torres,Astochasticschemeofapproximationforordinarydifferentialequations, ElectronicCommunicationsinProbabilityVol.13(2008)1–9. [7]R.Fierro,Aclassofstochasticepidemicmodelsanditsdeterministiccounterpart,Journal oftheKoreanStatisticalSocietyVol.39(No.4)(2010)397–407. [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,Annalesdel’InstitutHenri Poincaré(B)ProbabilitésetStatistiquesVol.13(No.2)(1977)171–179. [14]R.Rebolledo,Laméthodedesmartingalesappliquéeál’etudedelaconvergenceenloide processus,MémoiresdelaSociétéMathématiquedeFranceVol.62(No.4)(1979)1–125.