scholarly journals Pattern Theorems, Ratio Limit Theorems and Gumbel Maximal Clusters for Random Fields

2007 ◽  
Vol 130 (3) ◽  
pp. 503-522 ◽  
Author(s):  
Remco van der Hofstad ◽  
Wouter Kager
Keyword(s):  
Random Fields ◽  
Limit Theorems ◽  
Ratio Limit Theorems ◽  
Ratio Limit ◽  
Maximal Clusters

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 ◽  
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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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