  In this paper, we consider a class of stochastic midpoint and trapezoidal
Lawson schemes for the numerical discretization of highly oscillatory
stochastic differential equations. These Lawson schemes incorporate both the
linear drift and diffusion terms in the exponential operator. We prove that the
midpoint Lawson schemes preserve quadratic invariants and discuss this property
as well for the trapezoidal Lawson scheme. Numerical experiments demonstrate
that the integration error for highly oscillatory problems is smaller than that
of some standard methods.
