scholarly journals A Berry-Esséen theorem and a functional law of the iterated logarithm for weakly associated random vectors

1988 ◽  
Vol 30 (2) ◽  
pp. 277-289 ◽  
Author(s):  
AndréR. Dabrowski ◽  
Herold Dehling
Keyword(s):  
Random Vectors ◽  
Iterated Logarithm

scholarly journals The law of the iterated logarithm on subsequences-characterizations

1990 ◽  
Vol 118 ◽  
pp. 65-97 ◽  
Author(s):  
Michel Weber
Keyword(s):  
Unit Ball ◽  
Covariance Matrix ◽  
Identity Matrix ◽  
Random Vectors ◽  
Unbounded Function ◽  
Iterated Logarithm ◽  
Cluster Set ◽  
Euclidian Space ◽  
Zero Vector ◽  
Increasing Sequences

Let be any increasing sequence of integers and M> 1; we connect to them in a very simply way, an increasing unbounded function φ: → R+. Let also X1, X2, · · · be a sequence of i.i.d. random vectors with value in euclidian space Rm. We prove that the cluster set of the sequence almost surely coincides with the unit ball of Rm, if, and only if, the covariance matrix of X1 is the identity matrix of Rm and EX1 is the zero vector of Rm. We define a functional A on the set of increasing sequences of integers as follows:.

scholarly journals Compact Law of the Iterated Logarithm for Matrix-Normalized Sums of Random Vectors

2007 ◽  
Vol 52 (4) ◽  
pp. 752-767 ◽  
Author(s):  
Abdelkader Mokkadem ◽  
Abdelkader Mokkadem ◽  
Mariane Pelletier ◽  
Mariane Pelletier
Keyword(s):  
Random Vectors ◽  
Iterated Logarithm
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