  This paper considers the motion of an object subjected to dry friction and an
external random force. The objective is to characterize the role of the
correlation time of the external random force. We develop efficient stochastic
simulation methods for computing the diffusivity (the linear growth rate of the
variance of the displacement) and other related quantities of interest when the
external random force is white or colored. These methods are based on original
representation formulas for the quantities of interest which make it possible
to build unbiased and consistent estimators. The numerical results obtained
with these original methods are in perfect agreement with known closed-form
formulas valid in the white noise regime. In the colored noise regime the
numerical results show that the predictions obtained from the white-noise
approximation are reasonable for quantities such as the histograms of the
stationary velocity but can be wrong for the diffusivity unless the correlation
time is extremely small.
