scholarly journals On the prediction theory of two-parameter stationary random fields

1990 ◽  
Vol 32 (1) ◽  
pp. 120-149 ◽  
Author(s):  
G. Kallianpur ◽  
A.G. Miamee ◽  
H. Niemi
Keyword(s):  
Random Fields ◽  
Prediction Theory ◽  
Stationary Random Fields ◽  
Two Parameter

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.

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 Managing local dependencies in asymptotic theory for maxima of stationary random fields

Extremes ◽  
2018 ◽  
Vol 22 (2) ◽  
pp. 293-315 ◽  
Author(s):  
Adam Jakubowski ◽  
Natalia Soja-Kukieła
Keyword(s):  
Random Fields ◽  
Asymptotic Theory ◽  
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.

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