Sensitivity of the rate-distortion function of stationary continuous-time Gaussian processes to non-Gaussian contamination

Let S(N,Z) be the sensitivity of the rate-distortion function (relative to the mean-square-error criterion) of a continuous-time stationary Gaussian process N=N(t) to non-Gaussian contamination Z=Z(t). We prove that for any entropy-regular process Z the equality S(N,Z)=S(N,Z*) holds, where Z*=Z*(t) is a stationary Gaussian process with the same autocorrelation function as Z. An explicit expression for S(N,Z) in the terms of the spectral densities of N and Z is also derived. We also prove that S(N,Z)=0 for any entropy-singular process Z.