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...g-likelihhod vary together. In contrast, in [19], the expectation is taken with respect to a fixed parameter value. Given the interest in the analyticity results [4] for the discrete-alphabet setting =-=[8, 13, 15, 16, 19, 20]-=-, we expect that the results in this paper will be of significance for the continuousalphabet setting as well. The remainder of this paper is organized as follows. In Section 2, we review the (real) H...

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...-state channels. However, some of the basic problems, such as smoothness (or even differentiability) of H(Y ), have long remained unknown. Recently, asymptotical behavior of H(Y ) has been studied in =-=[3, 29, 39, 40, 56, 57, 38, 41, 44]-=-. Particularly in [56], for a special type of hidden Markov chain Y , the Taylor series expansion of H(Y ) is given under the assumption that H(Y ) is analytic. Under mild assumptions, analyticity of ...

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...µ on the inputs which could gave rise to ν. The two distributions may differ because information may be lost in the transmission. For examples of papers where this point of view is taken see [11] and =-=[13]-=-. Here, one role filled by thermodynamic formalism is to identify those measures µ which have maximal entropy given that they produced the observed output distribution ν. The entropy of µ then gives t...