Abstract
In this paper we establish a new local convergence theorem for partial sums of arbitrary stochastic adapted sequences. As corollaries, we generalize some recently obtained results and prove a limit theorem for the entropy density of an arbitrary information source, which is an extension of case of nonhomogeneous Markov chains.
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Yang, W., Ye, Z. & Liu, W. A local convergence theorem for partial sums of stochastic adapted sequences. Czech Math J 56, 525–532 (2006). https://doi.org/10.1007/s10587-006-0034-4
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DOI: https://doi.org/10.1007/s10587-006-0034-4