Uniformly accurate schemes for drift--oscillatory stochastic differential equations

Ibrahim Almuslimani (1, 2) , Philippe Chartier (3, 4) , Mohammed Lemou (2) , Florian Méhats (2)

1 UR Mathématiques - Université de Rennes - UFR Mathématiques
2 MINGUS - Multi-scale numerical geometric schemes
3 IRMAR - Institut de Recherche Mathématique de Rennes
4 Inria Rennes – Bretagne Atlantique

In this work, we adapt the micro-macro methodology to stochastic differential equations for the purpose of numerically solving oscillatory evolution equations. The models we consider are addressed in a wide spectrum of regimes where oscillations may be slow or fast. We show that through an ad-hoc transformation (the micro-macro decomposition), it is possible to retain the usual orders of convergence of Euler-Maruyama method, that is to say, uniform weak order one and uniform strong order one half.

Mots clés: highly-oscillatory; stochastic differential equations; micro-macro decomposition; uniform accuracy

Domaines: Mathématiques [math]; Analyse numérique [math.NA]

Ibrahim Almuslimani, Philippe Chartier, Mohammed Lemou, Florian Méhats. Uniformly accurate schemes for drift--oscillatory stochastic differential equations. 2021. ⟨hal-03371466v1⟩