scholarly journals An invariance principle for stationary random fields under Hannan’s condition

2014 ◽  
Vol 124 (12) ◽  
pp. 4012-4029 ◽  
Author(s):  
Dalibor Volný ◽  
Yizao Wang
Keyword(s):  
Invariance Principle ◽  
Random Fields ◽  
Stationary 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 via orthomartingale approximation

2018 ◽  
Vol 18 (06) ◽  
pp. 1850043 ◽  
Author(s):  
Davide Giraudo
Keyword(s):  
Invariance Principle ◽  
Random Fields ◽  
Partial Sums ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Stationary Random Fields ◽  
Necessary And Sufficient

We obtain a necessary and sufficient condition for the orthomartingale-coboundary decomposition. We establish a sufficient condition for the approximation of the partial sums of a strictly stationary random fields by those of stationary orthomartingale differences. This condition can be checked under multidimensional analogues of the Hannan condition and the Maxwell–Woodroofe condition.

Extremes of stationary random fields on a lattice

Extremes ◽  
2019 ◽  
Vol 22 (3) ◽  
pp. 391-411 ◽  
Author(s):  
Chengxiu Ling
Keyword(s):  
Random Fields ◽  
Stationary Random Fields

scholarly journals On the prediction error for two-parameter stationary random fields

1992 ◽  
Vol 46 (1) ◽  
pp. 167-175
Author(s):  
R. Cheng
Keyword(s):  
Random Fields ◽  
Prediction Error ◽  
Duality Relation ◽  
Stationary Random Fields ◽  
Error Formulas ◽  
Two Parameter ◽  
General Duality

A number of Szegö-type prediction error formulas are given for two-parameter stationary random fields. These give rise to an array of elementary inequalities and illustrate a general duality relation.

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
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