scholarly journals The mean Euler characteristic and excursion probability of Gaussian random fields with stationary increments

2016 ◽  
Vol 26 (2) ◽  
pp. 722-759 ◽  
Author(s):  
Dan Cheng ◽  
Yimin Xiao
Keyword(s):  
Euler Characteristic ◽  
Random Fields ◽  
Gaussian Random Fields ◽  
Stationary Increments ◽  
The Mean ◽  
Excursion Probability

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.

On Estimation of the Mean and Covariance Parameter for Gaussian Random Fields

Statistics ◽  
1998 ◽  
Vol 31 (1) ◽  
pp. 1-20 ◽  
Author(s):  
P. Ibarrola ◽  
R. Różański ◽  
R. Vélez
Keyword(s):  
Random Fields ◽  
Gaussian Random Fields ◽  
The Mean

The mean number of maxima above high levels in Gaussian random fields

1976 ◽  
Vol 13 (02) ◽  
pp. 377-379 ◽  
Author(s):  
A. M. Hasofer
Keyword(s):  
Asymptotic Formula ◽  
Random Fields ◽  
Gaussian Random Fields ◽  
Gaussian Field ◽  
General Proof ◽  
The Mean

An asymptotic formula for the mean number of maxima above a level of an n-dimensional stationary Gaussian field has been given by Nosko without proof. In this note a short general proof of this formula is given.

On Estimation of the Mean and Covariance Parameter for Gaussian Random Fields

Statistics ◽  
1999 ◽  
Vol 31 (1) ◽  
pp. 1-20
Author(s):  
P. Ibarrola ◽  
R. Rózanski ◽  
R. Vélez
Keyword(s):  
Random Fields ◽  
Gaussian Random Fields ◽  
The Mean

About approximation of 3-D random fields and statistical simulation

2003 ◽  
Vol 11 (3) ◽  
Author(s):  
Zoya O. Vyzhva
Keyword(s):  
Random Fields ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Statistical Simulation ◽  
Gaussian Random Fields ◽  
Statistical Characteristics ◽  
Mean Square ◽  
The Mean ◽  
Isotropic Random ◽  
Three Dimensional Space

The estimator of the mean-square approximation of 3-D homogeneous and isotropic random field is investigated. The problem of statistical simulation of realizations of random fields in threedimensional space is considered. The algorithm for the receiving of this realization has been formulated, which has been constructed on the base the mean-square approximation of random fields estimator. It has been constructed the statistical model for the Gaussian random fields in three-dimensional space, which has been given by its statistical characteristics.

scholarly journals CHARACTERIZATION OF THE FORMATION OF FILTER PAPER USING THE BARTLETT SPECTRUM OF THE FIBER STRUCTURE

2013 ◽  
Vol 32 (2) ◽  
pp. 77 ◽  
Author(s):  
Martin Lehmann ◽  
Jobst Eisengräber-Pabst ◽  
Joachim Ohser ◽  
Ali Moghiseh
Keyword(s):  
Quality Control ◽  
Filter Paper ◽  
Random Fields ◽  
Image Data ◽  
Gaussian Random Fields ◽  
Fiber Structure ◽  
Bessel Transform ◽  
The Mean ◽  
Paper Structure

The formation index of filter paper is one of the most important characteristics used in industrial quality control. Its estimation is often based on subjective comparison chart rating or, even more objective, on the power spectrum of the paper structure observed on a transmission light table. It is shown that paper formation can be modeled as Gaussian random fields with a well defined class of correlation functions, and a formation index can be derived from the density of the Bartlett spectrum estimated from image data. More precisely, the formation index is the mean of the Bessel transform of the correlation taken for wave lengths between 2 and 5 mm.

The mean number of maxima above high levels in Gaussian random fields

1976 ◽  
Vol 13 (2) ◽  
pp. 377-379 ◽  
Author(s):  
A. M. Hasofer
Keyword(s):  
Asymptotic Formula ◽  
Random Fields ◽  
Gaussian Random Fields ◽  
Gaussian Field ◽  
General Proof ◽  
The Mean

An asymptotic formula for the mean number of maxima above a level of an n-dimensional stationary Gaussian field has been given by Nosko without proof. In this note a short general proof of this formula is given.

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