On the Rate of Convergence to Normal Law which is Equivalent to the Existence of a Second Moment

1973 ◽  
Vol 18 (1) ◽  
pp. 175-180 ◽  
Author(s):  
V. A. Egorov
Keyword(s):  
Rate Of Convergence ◽  
Second Moment ◽  
Normal Law

scholarly journals Davis-type theorems for martingale difference sequences

2005 ◽  
Vol 2005 (2) ◽  
pp. 159-165 ◽  
Author(s):  
George Stoica
Keyword(s):  
Rate Of Convergence ◽  
Classical Case ◽  
Moderate Deviation ◽  
Sharp Contrast ◽  
Optimal Rate ◽  
Martingale Difference ◽  
Normalization Factor ◽  
Second Moment ◽  
Optimal Rate Of Convergence ◽  
Difference Sequences

We study Davis-type theorems on the optimal rate of convergence of moderate deviation probabilities. In the case of martingale difference sequences, under the finite pth moments hypothesis (1≤p<∞), and depending on the normalization factor, our results show that Davis' theorems either hold if and only if p>2 or fail for all p≥1. This is in sharp contrast with the classical case of i.i.d. centered sequences, where both Davis' theorems hold under the finite second moment hypothesis (or less).

Rate of convergence of quasistable laws to the normal law

1988 ◽  
Vol 40 (4) ◽  
pp. 573-580
Author(s):  
O. L. Yanushkyavichene
Keyword(s):  
Rate Of Convergence ◽  
Normal Law

scholarly journals The rate of convergence to the normal law in terms of pseudomoments

2015 ◽  
Vol 2 (2) ◽  
pp. 95-106
Author(s):  
Yuliya Mishura ◽  
Yevheniya Munchak ◽  
Petro Slyusarchuk
Keyword(s):  
Rate Of Convergence ◽  
Normal 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.

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