Invariance principle for certain classes of random fields

1980 ◽  
Vol 31 (5) ◽  
pp. 443-448
Author(s):  
N. N. Leonenko ◽  
M. I. Yadrenko
Keyword(s):  
Invariance Principle ◽  
Random Fields

On the weak invariance principle for non-adapted stationary random fields under projective criteria

2021 ◽  
Author(s):  
Han-Mai Lin
Keyword(s):  
Invariance Principle ◽  
Random Fields ◽  
Long Memory ◽  
Sufficient Conditions ◽  
Weak Invariance Principle ◽  
Weak Invariance ◽  
The Central Limit Theorem ◽  
Projective Criteria ◽  
Stationary Random Fields ◽  
Do So

In this paper, we study the central limit theorem (CLT) and its weak invariance principle (WIP) for sums of stationary random fields non-necessarily adapted, under different normalizations. To do so, we first state sufficient conditions for the validity of a suitable ortho-martingale approximation. Then, with the help of this approximation, we derive projective criteria under which the CLT as well as the WIP hold. These projective criteria are in the spirit of Hannan’s condition and are well adapted to linear random fields with ortho-martingale innovations and which exhibit long memory.

scholarly journals Invariance principle for associated random fields

1996 ◽  
Vol 81 (5) ◽  
pp. 2905-2911 ◽  
Author(s):  
A. V. Bulinski ◽  
M. S. Keane
Keyword(s):  
Invariance Principle ◽  
Random Fields
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