  We prove that under certain mild assumptions, the entropy rate of a hidden
Markov chain, observed when passing a finite-state stationary Markov chain
through a discrete-time continuous-output channel, is jointly analytic as a
function of the input Markov chain parameters and the channel parameters. In
particular, as consequences of the main theorems, we obtain analyticity for the
entropy rate associated with representative channels: Cauchy and Gaussian.
