On strong limit theorems for general information sources with an application to AEP

Zhong-Zhi Wang, Shan-Shan Yang, Hai-Feng Jiang and Fang-Qing Ding

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 6, 1387-1399

Abstract: In this article we prove some strong law of large numbers of arithmetic and geometric mean for a sequence of general information source X={Xn}n∈N. Under some appropriate conditions, we also obtain a strong limit theorem on harmonic mean of the transition probabilities of X. Finally, as a simple application to information theory, we establish some asymptotic equipartition properties for the generalized entropy density of information sources.

Date: 2021
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DOI: 10.1080/03610926.2019.1650186

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