On the Invariance Principle for Homogeneous and Isotropic Random Fields

1979 ◽  
Vol 24 (1) ◽  
pp. 175-181 ◽  
Author(s):  
N. N. Leonenko ◽  
M. I. Yadrenko
Keyword(s):  
Invariance Principle ◽  
Random Fields ◽  
Isotropic Random

scholarly journals Needlet approximation for isotropic random fields on the sphere

2017 ◽  
Vol 216 ◽  
pp. 86-116 ◽  
Author(s):  
Quoc T. Le Gia ◽  
Ian H. Sloan ◽  
Yu Guang Wang ◽  
Robert S. Womersley
Keyword(s):  
Random Fields ◽  
Isotropic Random

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

scholarly journals Identification and isotropy characterization of deformed random fields through excursion sets

2018 ◽  
Vol 50 (3) ◽  
pp. 706-725
Author(s):  
Julie Fournier
Keyword(s):  
Random Field ◽  
Euler Characteristic ◽  
Random Fields ◽  
Weak Form ◽  
Invariance Property ◽  
Basic Domain ◽  
Excursion Sets ◽  
The Mean ◽  
Isotropic Random

Abstract A deterministic application θ:ℝ2→ℝ2 deforms bijectively and regularly the plane and allows the construction of a deformed random field X∘θ:ℝ2→ℝ from a regular, stationary, and isotropic random field X:ℝ2→ℝ. The deformed field X∘θ is, in general, not isotropic (and not even stationary), however, we provide an explicit characterization of the deformations θ that preserve the isotropy. Further assuming that X is Gaussian, we introduce a weak form of isotropy of the field X∘θ, defined by an invariance property of the mean Euler characteristic of some of its excursion sets. We prove that deformed fields satisfying this property are strictly isotropic. In addition, we are able to identify θ, assuming that the mean Euler characteristic of excursion sets of X∘θ over some basic domain is known.

scholarly journals An efficient maximum entropy technique for 2-D isotropic random fields

1988 ◽  
Vol 36 (5) ◽  
pp. 797-812 ◽  
Author(s):  
A.H. Tewfik ◽  
B.C. Levy ◽  
A.S. Willsky
Keyword(s):  
Maximum Entropy ◽  
Random Fields ◽  
Entropy Technique ◽  
Isotropic Random

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.

Cross‐dimple in the cross‐covariance functions of bivariate isotropic random fields on spheres

Stat ◽  
2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Alfredo Alegría
Keyword(s):  
Random Fields ◽  
Covariance Functions ◽  
Cross Covariance ◽  
The Cross ◽  
Isotropic Random

Stochastic filling of homogeneous isotropic random fields

2006 ◽  
Vol 21 (6) ◽  
Author(s):  
N. I. Gubina ◽  
V. A. Ogorodnikov
Keyword(s):  
Random Fields ◽  
Isotropic Random
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