Rate of convergence in the invariance principle for martingale difference arrays

1994 ◽  
Vol 34 (4) ◽  
pp. 383-392
Author(s):  
K. Kubilius
Keyword(s):  
Rate Of Convergence ◽  
Invariance Principle ◽  
Martingale Difference

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).

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