Representation of random processes by complete orthonormal sequences

For a random process x(t) with autocorrelation function R(s, t) satisfying ∫
I
R(t, t) dt < + ∞, the generalized Fourier expansion of x(t) in any complete orthonormal sequence of L
2
functions on I converges to x(t) in an integral mean-square sense on I. This generalizes a result due to Young, on the use of orthonormalized exponentials in representing random processes.