A Strong Limit Theorem for Functions of Continuous Random Variables and an Extension of the Shannon-McMillan Theorem
Gaorong Li, Shuang Chen, and Sanying Feng
Source: J. Appl. Math. Volume 2008
(2008), Article ID
639145, 10 pages.
Abstract
By means of the notion of likelihood ratio, the limit properties of the sequences of arbitrary-dependent continuous random variables are studied, and a kind of strong limit theorems represented by inequalities with random bounds for functions of continuous random variables is established. The Shannon-McMillan theorem is extended to the case of arbitrary continuous information sources. In the proof, an analytic technique, the tools of Laplace transform, and moment generating functions to study the strong limit theorems are applied.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jam/1220969292
Digital Object Identifier: doi:10.1155/2008/639145
Mathematical Reviews number (MathSciNet): MR2399309
Zentralblatt MATH identifier: 1145.60309
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