scholarly journals Limit Theorems for Excursion Sets of Stationary Random Fields

2013 ◽  
pp. 221-241 ◽  
Author(s):  
Evgeny Spodarev
Keyword(s):  
Random Fields ◽  
Limit Theorems ◽  
Excursion Sets ◽  
Stationary Random Fields

scholarly journals Orthomartingale-coboundary decomposition for stationary random fields

2016 ◽  
Vol 16 (05) ◽  
pp. 1650017 ◽  
Author(s):  
Mohamed El Machkouri ◽  
Davide Giraudo
Keyword(s):  
Large Deviations ◽  
Random Field ◽  
Random Fields ◽  
Decomposition Method ◽  
Limit Theorems ◽  
Stationary Random Fields

We provide a new projective condition for a stationary real random field indexed by the lattice [Formula: see text] to be well approximated by an orthomartingale in the sense of Cairoli (1969). Our main result can be viewed as a multidimensional version of the martingale-coboundary decomposition method which the idea goes back to Gordin (1969). It is a powerful tool for proving limit theorems or large deviations inequalities for stationary random fields when the corresponding result is valid for orthomartingales.

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 perimeter of excursion sets of shot noise random fields

2016 ◽  
Vol 44 (1) ◽  
pp. 521-543 ◽  
Author(s):  
Hermine Biermé ◽  
Agnès Desolneux
Keyword(s):  
Shot Noise ◽  
Random Fields ◽  
Excursion Sets

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 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 Excursion sets of infinitely divisible random fields with convolution equivalent Lévy measure

2017 ◽  
Vol 54 (3) ◽  
pp. 833-851 ◽  
Author(s):  
Anders Rønn-Nielsen ◽  
Eva B. Vedel Jensen
Keyword(s):  
Random Field ◽  
Large Class ◽  
Random Fields ◽  
Lévy Measure ◽  
Infinitely Divisible ◽  
Excursion Sets ◽  
Excursion Set ◽  
Fixed Radius ◽  
Asymptotic Probability ◽  
The Right

Abstract We consider a continuous, infinitely divisible random field in ℝd, d = 1, 2, 3, given as an integral of a kernel function with respect to a Lévy basis with convolution equivalent Lévy measure. For a large class of such random fields, we compute the asymptotic probability that the excursion set at level x contains some rotation of an object with fixed radius as x → ∞. Our main result is that the asymptotic probability is equivalent to the right tail of the underlying Lévy measure.

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