On Asymptotic Preserving schemes for a class of Stochastic Differential Equations in averaging and diffusion approximation regimes
| Autor: | Charles-Edouard Bréhier, Shmuel Rakotonirina-Ricquebourg |
|---|---|
| Přispěvatelé: | Bréhier, Charles-Edouard, Bords, oscillations et couches limites dans les systèmes différentiels - - BORDS2016 - ANR-16-CE40-0027 - AAPG2016 - VALID, Simulation aléatoire en dimension infinie - - SIMALIN2019 - ANR-19-CE40-0016 - AAPG2019 - VALID, Moyennisation, approximation-diffusion en dimension infinie - théorie et approximation numérique - - ADA2019 - ANR-19-CE40-0019 - AAPG2019 - VALID, Probabilités, statistique, physique mathématique (PSPM), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), ANR-16-CE40-0027,BORDS,Bords, oscillations et couches limites dans les systèmes différentiels(2016), ANR-19-CE40-0016,SIMALIN,Simulation aléatoire en dimension infinie(2019), ANR-19-CE40-0019,ADA,Moyennisation, approximation-diffusion en dimension infinie - théorie et approximation numérique(2019) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]
averaging principle Ecological Modeling Probability (math.PR) diffusion approximation weak approximation AMS subject classifications General Physics and Astronomy General Chemistry Numerical Analysis (math.NA) [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA] Computer Science Applications [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Modeling and Simulation slow-fast Stochastic Differ- ential Equations FOS: Mathematics multiscale methods Asymptotic preserving schemes Mathematics - Numerical Analysis [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] Mathematics - Probability |
| Popis: | We introduce and study a notion of Asymptotic Preserving schemes, related to convergence in distribution, for a class of slow-fast Stochastic Differential Equations. In some examples , crude schemes fail to capture the correct limiting equation resulting from averaging and diffusion approximation procedures. We propose examples of Asymptotic Preserving schemes: when the timescale separation vanishes, one obtains a limiting scheme, which is shown to be consistent in distribution with the limiting Stochastic Differential Equation. Numerical experiments illustrate the importance of the proposed Asymptotic Preserving schemes for several examples. In addition, in the averaging regime, error estimates are obtained and the proposed scheme is proved to be uniformly accurate. |
| Databáze: | OpenAIRE |
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