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

Lawson schemes for highly oscillatory stochastic differential equations and conservation of invariants