scholarly journals On the rosenthal inequality for mixing fields

2000 ◽  
Vol 52 (2) ◽  
pp. 305-318 ◽  
Author(s):  
I. Fazekas ◽  
A. G. Kukush ◽  
T. Tómács
Keyword(s):  
Rosenthal Inequality

Rosenthal inequality for NOD sequences and its applications

2011 ◽  
Vol 16 (3) ◽  
pp. 185-189 ◽  
Author(s):  
Shixin Gan ◽  
Pingyan Chen ◽  
Dehua Qiu
Keyword(s):  
Rosenthal Inequality

scholarly journals Complete Moment Convergence and Mean Convergence for Arrays of Rowwise Extended Negatively Dependent Random Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yongfeng Wu ◽  
Mingzhu Song ◽  
Chunhua Wang
Keyword(s):  
Random Variables ◽  
Complete Moment Convergence ◽  
Dependent Random Variables ◽  
Rosenthal Inequality ◽  
Mean Convergence ◽  
Moment Convergence ◽  
Negatively Dependent Random Variables ◽  
Convergence Results ◽  
End Random Variables

The authors first present a Rosenthal inequality for sequence of extended negatively dependent (END) random variables. By means of the Rosenthal inequality, the authors obtain some complete moment convergence and mean convergence results for arrays of rowwise END random variables. The results in this paper extend and improve the corresponding theorems by Hu and Taylor (1997).

scholarly journals A deviation bound for α-dependent sequences with applications to intermittent maps

2016 ◽  
Vol 17 (01) ◽  
pp. 1750005 ◽  
Author(s):  
Jérôme Dedecker ◽  
Florence Merlevède
Keyword(s):  
Large Deviations ◽  
Invariance Principle ◽  
Upper Bounds ◽  
Partial Sums ◽  
Rosenthal Inequality ◽  
Deviation Inequality ◽  
Mixing Sequences

We prove a deviation bound for the maximum of partial sums of functions of [Formula: see text]-dependent sequences as defined in [2]. As a consequence, we extend the Rosenthal inequality of Rio [16] for [Formula: see text]-mixing sequences in the sense of Rosenblatt [18] to the larger class of [Formula: see text]-dependent sequences. Starting from the deviation inequality, we obtain upper bounds for large deviations and Hölderian invariance principle for the Donsker line. We illustrate our results through the example of intermittent maps of the interval, which are not [Formula: see text]-mixing in the sense of Rosenblatt.

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