Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

ON ASYMPTOTIC PRESERVING SCHEMES FOR A CLASS OF STOCHASTIC DIFFERENTIAL EQUATIONS IN AVERAGING AND DIFFUSION APPROXIMATION REGIMES

Abstract : 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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [35 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02988284
Contributor : Charles-Edouard Bréhier <>
Submitted on : Wednesday, November 4, 2020 - 4:15:58 PM
Last modification on : Monday, November 9, 2020 - 11:14:02 AM

File

paper.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02988284, version 1

Citation

Charles-Edouard Bréhier, Shmuel Rakotonirina-Ricquebourg. ON ASYMPTOTIC PRESERVING SCHEMES FOR A CLASS OF STOCHASTIC DIFFERENTIAL EQUATIONS IN AVERAGING AND DIFFUSION APPROXIMATION REGIMES. 2020. ⟨hal-02988284⟩

Share

Metrics

Record views

14

Files downloads

12