scholarly journals A strong limit theorem expressed by inequalities for the sequences of absolutely continuous random variables

2002 ◽  
Vol 32 (3) ◽  
pp. 379-387 ◽  
Author(s):  
Wen Liu ◽  
Yujin Wang
Keyword(s):  
Limit Theorem ◽  
Random Variables ◽  
Strong Limit ◽  
Absolutely Continuous ◽  
Strong Limit Theorem

scholarly journals A Strong Limit Theorem for Functions of Continuous Random Variables and an Extension of the Shannon-McMillan Theorem

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
Gaorong Li ◽  
Shuang Chen ◽  
Sanying Feng
Keyword(s):  
Limit Theorem ◽  
Laplace Transform ◽  
Likelihood Ratio ◽  
Generating Functions ◽  
Limit Theorems ◽  
Information Sources ◽  
Random Variables ◽  
Strong Limit ◽  
Moment Generating Functions ◽  
Strong Limit Theorem

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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