In this study, a class of strong limit theorems for the relative entropy densities of random sum of arbitrary information source are discussed by constructing the joint distribution and nonnegative super martingales. As corollaries, some Shannon-McMillan theorems for arbitrary information source, mth-order Markov information source and non-memory information source are obtained and some results for the discrete information source which have been obtained by authors are extended.
Shannon-McMillan theorem, the consistent distribution, arbitrary information source, relative entropy density, m-order Markov information source, non-memory information source
"A class of generalized Shannon-McMillan theorems for arbitrary discrete information source,"
Turkish Journal of Mathematics: Vol. 35:
4, Article 13.
Available at: https://journals.tubitak.gov.tr/math/vol35/iss4/13