  We provide a method for calculating time-averaged stress fluctuations on
surfaces in a viscous incompressible fluid at equilibrium. We assume that (i)
the time-averaged fluctuating stress is balanced in equilibrium at each
position and that (ii) the time-averaged fluctuating stress obeys a Gaussian
distribution on the restricted configuration space given by (i). Using these
assumptions with the Green-Kubo formula for the viscosity, we can derive the
large deviation function of the time-averaged fluctuating stress. Then, using
the saddle-point method for the large deviation function, we obtain the
time-averaged surface stress fluctuations. As an example, for a fluid between
two parallel plates, we study the time-averaged shear/normal stress
fluctuations per unit area on the top plate at equilibrium. We show that the
surface shear/normal stress fluctuations are inversely proportional to the
distance between the plates.
