Log-periodogram regression of two-dimensional intrinsically stationary random fields

2020 ◽  
Vol 3 (1) ◽  
pp. 333-347
Author(s):  
Yoshihiro Yajima ◽  
Yasumasa Matsuda
Keyword(s):  
Random Fields ◽  
Two Dimensional ◽  
Stationary Random Fields

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.

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

scholarly journals Characterizing sand ripples at equilibrium phases

2013 ◽  
Vol 61 (4) ◽  
pp. 293-298 ◽  
Author(s):  
Jie Qin ◽  
Deyu Zhong ◽  
Guangqian Wang
Keyword(s):  
Time Series ◽  
Random Fields ◽  
Morphological Characteristics ◽  
Structure Functions ◽  
Second Order ◽  
Order Structure ◽  
Two Dimensional ◽  
Sand Ripples ◽  
Digital Elevation ◽  
Equilibrium Phases

Abstract Morphological characteristics of ripples are analyzed considering bed surfaces as two dimensional random fields of bed elevations. Two equilibrium phases are analyzed with respect to successive development of ripples based on digital elevation models. The key findings relate to the shape of the two dimensional second-order structure functions and multiscaling behavior revealed by higher-order structure functions. Our results suggest that (1) the two dimensional second-order structure functions can be used to differentiate the two equilibrium phases of ripples; and (2) in contrast to the elevational time series of ripples that exhibit significant multiscaling behavior, the DEMs of ripples at both equilibrium phases do not exhibit multiscaling behavior.

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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