  Expressions for (EPI Shannon type) Divergence-Power Inequalities (DPI) in two
cases (time-discrete and band-limited time-continuous) of stationary random
processes are given. The new expressions connect the divergence rate of the sum
of independent processes, the individual divergence rate of each process, and
their power spectral densities. All divergences are between a process and a
Gaussian process with same second order statistics, and are assumed to be
finite. A new proof of the Shannon entropy-power inequality EPI, based on the
relationship between divergence and causal minimum mean-square error (CMMSE) in
Gaussian channels with large signal-to-noise ratio, is also shown.
