# Multirevolution integrators for differential equations with fast stochastic oscillations

## TL;DR

This paper presents a novel multirevolution method for efficiently solving stochastic differential equations with fast oscillations driven by noise, achieving high accuracy and invariance preservation.

## Contribution

It introduces a new multirevolution integrator for stochastic oscillatory equations, with weak order two and invariant-preserving modifications, independent of oscillation stiffness.

## Key findings

- Achieves weak order two accuracy
- Computational cost independent of oscillation stiffness
- Exact preservation of quadratic invariants

## Abstract

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. Applications include in particular highly-oscillatory Kubo oscillators and spatial discretizations of the nonlinear Schr\"odinger equation with fast white noise dispersion. We construct a method of weak order two with computational cost and accuracy both independent of the stiffness of the oscillations. A geometric modification that conserves exactly quadratic invariants is also presented.