Correlation functions on the upper half space

The boundary condition and solution of a Dirichlet problem on the upper half space are treated as random processes. It is shown that the first-and second-order statistics of the solution to this problem are completely determined by the corresponding statistics of the boundary condition. The mean of the solution is the mean of the process on the boundary. The correlation function of the solution above the boundary is related to its value on the boundary by a Poisson integral formula. formerly of The Analytic Sciences Corporation, Reading, Massachusetts 01867. This research was supported in part by the Naval Weapons Laboratory, Dahlgren, Virginia, under Contract N00178-70-C-0200.