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

Approximation of some discrete-time stochastic processes by differential equations

Raúl FİERRO
Pages
1035–1046
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Thisworkdealswithsolutionsofordinarydifferentialequationsasapproximationsofsomediscrete-timestochasticprocesses.Similarly,thesestochasticprocessesmaybeseenasschemesofapproximationforthissolution.Indeed,thesestochasticschemesaredefinedandtheirconvergencetothesolutionofadifferentialequationisproven.More-over,theasymptoticdistributionofthefluctuationsaboutthelimitsolutionisstudied.Thisfactgivestheasymptoticdistributionofarandomglobalerrorofapproximation.MainresultsareillustratedbymeansofthesocalledSISepidemicmodelandnumericalsimulationsarecarriedout.
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Key Findings & Data:Thisworkdealswithsolutionsofordinarydifferentialequationsasapproximationsofsomediscrete-timestochasticprocesses.Similarly,thesestochasticprocessesmaybeseenasschemesofapproximationforthissolution.Indeed,thesestochasticschemesaredefinedandtheirconvergencetothesolutionofadifferentialequationisproven.More-over,theasymptoticdistributionofthefluctuationsaboutthelimitsolutionisstudied.Thisfactgivestheasymptoticdistributionofarandomglobalerrorofapproximation.MainresultsareillustratedbymeansofthesocalledSISepidemicmodelandnumericalsimulationsarecarriedout.
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Conclusion & Impact:Thisworkdealswithsolutionsofordinarydifferentialequationsasapproximationsofsomediscrete-timestochasticprocesses.Similarly,thesestochasticprocessesmaybeseenasschemesofapproximationforthissolution.Indeed,thesestochasticschemesaredefinedandtheirconvergencetothesolutionofadifferentialequationisproven.More-over,theasymptoticdistributionofthefluctuationsaboutthelimitsolutionisstudied.Thisfactgivestheasymptoticdistributionofarandomglobalerrorofapproximation.MainresultsareillustratedbymeansofthesocalledSISepidemicmodelandnumericalsimulationsarecarriedout.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

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

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Cite This Article

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

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References (1)

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