On the numerical discretisation of stochastic oscillators

In this article, we propose an approach, based on the variation‐of‐constants formula, for the numerical discretisation over long‐time intervals of several stochastic oscillators. Additive and multiplicative noises are treated separately. The proposed schemes permit the use of large step sizes in the presence of a high frequency in the problem and offer various additional properties. These new numerical integrators can be viewed as a stochastic‐generalisation of the trigonometric integrators for highly oscillatory deterministic problems.