scholarly journals Ratio limit theorems and Tauberian theorems for vector-valued functions and sequences

2010 ◽  
Vol 367 (1) ◽  
pp. 108-115
Author(s):  
Jeng-Chung Chen ◽  
Ryotaro Sato
Keyword(s):  
Limit Theorems ◽  
Tauberian Theorems ◽  
Ratio Limit Theorems ◽  
Ratio Limit ◽  
Vector Valued Functions ◽  
Vector Valued

Ratio Limit Theorems

1976 ◽  
Vol 28 (2) ◽  
pp. 403-407
Author(s):  
A. G. Mucci
Keyword(s):  
Limit Theorems ◽  
Probability Space ◽  
Random Variables ◽  
Ratio Limit Theorems ◽  
Ratio Limit ◽  
Image Position

Let be an adapted sequence of integrable random variables on the probability space . Let us set .The following result can be immediately derived from Brown [2]:

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