A law of the iterated logarithm for heavy-tailed random vectors

2000 ◽  
Vol 116 (2) ◽  
pp. 257-271 ◽  
Author(s):  
Hans-Peter Scheffler
Keyword(s):  
Random Vectors ◽  
Iterated Logarithm ◽  
Heavy Tailed

scholarly journals Large deviation probabilities for sums of heavy-tailed dependent random vectors

1997 ◽  
Vol 13 (4) ◽  
pp. 647-660 ◽  
Author(s):  
Adam Jakubowski ◽  
Alexander. V. Nagaev ◽  
Zaigraev Alexander
Keyword(s):  
Large Deviation ◽  
Random Vectors ◽  
Large Deviation Probabilities ◽  
Heavy Tailed

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:.

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