Rate of convergence in the law of large numbers in banach spaces

1982 ◽  
Vol 22 (2) ◽  
pp. 105-111
Author(s):  
G. Bakštys ◽  
R. Norvaiša
Keyword(s):  
Rate Of Convergence ◽  
Banach Spaces ◽  
Law Of Large Numbers ◽  
Large Numbers ◽  
The Law

scholarly journals On the rate of convergence in the strong law of large numbers for arrays

1992 ◽  
Vol 45 (3) ◽  
pp. 479-482 ◽  
Author(s):  
Tien-Chung Hu ◽  
N.C. Weber
Keyword(s):  
Rate Of Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Strong Law ◽  
Second Moment ◽  
Iterated Logarithm ◽  
Large Numbers ◽  
The Law ◽  
Independent And Identically Distributed

For sequences of independent and identically distributed random variables it is well known that the existence of the second moment implies the law of the iterated logarithm. We show that the law of the iterated logarithm does not extend to arrays of independent and identically distributed random variables and we develop an analogous rate result for such arrays under finite fourth moments.

scholarly journals Tauberian theorems for summability transforms

2005 ◽  
Vol 2005 (1) ◽  
pp. 55-66
Author(s):  
Rohitha Goonatilake
Keyword(s):  
Random Walk ◽  
Rate Of Convergence ◽  
Law Of Large Numbers ◽  
Summability Method ◽  
Tauberian Theorems ◽  
Strong Law ◽  
Random Walk Method ◽  
Large Numbers ◽  
The Law

The convolution summability method is introduced as a generalization of the random-walk method. In this paper, two well-known summability analogs concerning the strong law of large numbers (SLLN) and the law of the single logarithm (LSL), that gives the rate of convergence in SLLN for the random-walk method, are extended to this generalized method.

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