Open AccessA Strong Limit Theorem for Functions of Continuous Random Variables and an Extension of the Shannon‐McMillan Theorem
Author(s) -
Gaorong Li,
Shuang Chen,
Sanying Feng
Publication year - 2008
Publication title -
journal of applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.307
H-Index - 43
eISSN - 1687-0042
pISSN - 1110-757X
DOI - 10.1155/2008/639145
Subject(s) - mathematics , limit (mathematics) , random variable , extension (predicate logic) , laplace transform , central limit theorem , illustration of the central limit theorem , moment (physics) , uniform limit theorem , discrete mathematics , convergence of random variables , pure mathematics , sum of normally distributed random variables , mathematical analysis , statistics , quantum mechanics , computer science , physics , programming language
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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