Distribution of the time-average power of a Gaussian process

A method is given for obtaining a closed-form expression for the characteristic function of the average power, in a
T
-second interval, of a zero-mean Gaussian random process. The technique, which is constructive in nature, is applicable to the class of covariance kernels whose corresponding homogeneous Fredholm integral equations admit reduction to an equivalent linear differential system. Eigenvalue evaluations are not required.