Multirevolution integrators for differential equations with fast stochastic oscillations

Initially created in the context of celestial mechanics and later extended using geometric integration, multirevolution methods represent a class of numerical methods used for solving highly-oscillatory differential equations while reducing the cost of computation.
In this talk, we introduce a new methodology based on the multirevolution idea for constructing integrators for stochastic differential equations in the situation where the fast oscillations themselves are driven by a Stratonovich noise.
We will build together two new methods adapted for highly oscillatory SDEs, and will test their accuracy in particular on highly-oscillatory Kubo oscillators and spatial discretizations of nonlinear Schrödinger equation with fast white noise dispersion.