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We consider a random surface in R d tessellating the space into cells and a random vector eld u which is smooth on each cell but may jump on. Assuming the pair ((; u) stationary we prove a relationship between the stationary probability measure P and the Palm probability measure P of P with respect to the random surface measure associated with. This result involves the ow of u induced on the individual cells and generalizes a well-known inversion formula for stationary point processes on the line. An immediate consequence of this result is a formula for certain generalized contact distribution functions of , and as rst application we prove a result on the spherical contact distribution in stochastic geometry. As another application we prove an invariance property for P which again generalizes a corresponding property in dimension d = 1. Under the assumption that the ow can be deened for all time points, we consider the point process N of sucessive crossing times starting in the origin 0. If the ow is volume-preserving, then N is stationary and we express its Palm probability in terms of P .

On stationary stochastic flows and Palm probabilities of surface processes