  We propose a general variance reduction strategy for diffusion processes. Our
approach does not require the knowledge of the measure that is sampled, which
may indeed be unknown as for nonequilibrium dynamics in statistical physics. We
show by a perturbative argument that a control variate computed for a
simplified version of the model can provide an efficient control variate for
the actual problem at hand. We illustrate our method with numerical experiments
and show how the control variate is built in three practical cases: the
computation of the mobility of a particle in a periodic potential; the thermal
flux in atom chains, relying on a harmonic approximation; and the mean length
of a dimer in a solvent under shear, using a non-solvated dimer as the
approximation.
