  Sliding motion is evolution on a switching manifold of a discontinuous,
piecewise-smooth system of ordinary differential equations. In this paper we
quantitatively study the effects of small-amplitude, additive, white Gaussian
noise on stable sliding motion. For equations that are static in directions
parallel to the switching manifold, the distance of orbits from the switching
manifold approaches a quasi-steady-state density. From this density we
calculate the mean and variance for the near sliding solution. Numerical
results of a relay control system reveal that the noise may significantly
affect the period and amplitude of periodic solutions with sliding segments.
