Simulation of Multivariate Gaussian Fields Conditioned by Realizations of the Fields and Their Derivatives

1996 ◽  
Vol 63 (3) ◽  
pp. 758-765 ◽  
Author(s):  
Y. J. Ren ◽  
I. Elishakoff ◽  
M. Shinozuka
Keyword(s):  
Random Field ◽  
Random Fields ◽  
Conditional Simulation ◽  
Gaussian Random Fields ◽  
Gaussian Field ◽  
Interpolation Technique ◽  
Multivariate Gaussian ◽  
Component Field ◽  
Multivariate Gaussian Random Fields ◽  
First Time

This paper investigates conditional simulation technique of multivariate Gaussian random fields by stochastic interpolation technique. For the first time in the literature a situation is studied when the random fields are conditioned not only by a set of realizations of the fields, but also by a set of realizations of their derivatives. The kriging estimate of multivariate Gaussian field is proposed, which takes into account both the random field as well as its derivative. Special conditions are imposed on the kriging estimate to determine the kriging weights. Basic formulation for simulation of conditioned multivariate random fields is established. As a particular case of uncorrelated components of multivariate field without realizations of the derivative of the random field, the present formulation includes that of univariate field given by Hoshiya. Examples of a univariate field and a three component field are elucidated and some numerical results are discussed. It is concluded that the information on the derivatives may significantly alter the results of the conditional simulation.

scholarly journals Parametric Estimation of Long Memory Multivariate Gaussian random fields

2021 ◽  
Vol 16 (2) ◽  
pp. 2747-2761
Author(s):  
Aubin Yao N'dri ◽  
Amadou Kamagaté ◽  
Ouagnina Hili
Keyword(s):  
Random Fields ◽  
Long Memory ◽  
Almost Sure Convergence ◽  
Gaussian Random Fields ◽  
Parametric Estimation ◽  
Multivariate Gaussian ◽  
Finite Set ◽  
Multivariate Gaussian Random Fields ◽  
Distance Estimator ◽  
Set Of Points

The aim of this paper is to make a theoretically study of the minimum Hellinger distance estimator of multivariate, gaussian, stationary, isotropic long-memory random fields The variables are observed on a finite set of points in space. We establish under certain assumptions, the almost sure convergence and the asymptotic distribution of this estimator.

scholarly journals Parametric Estimation of Long Memory Multivariate Gaussian random fields

2021 ◽  
Vol 16 (2) ◽  
pp. 2749-2766
Author(s):  
Aubin Yao N'dri ◽  
Amadou Kamagaté ◽  
Ouagnina Hili
Keyword(s):  
Random Fields ◽  
Long Memory ◽  
Almost Sure Convergence ◽  
Gaussian Random Fields ◽  
Parametric Estimation ◽  
Multivariate Gaussian ◽  
Finite Set ◽  
Multivariate Gaussian Random Fields ◽  
Distance Estimator ◽  
Set Of Points

The aim of this paper is to make a theoretically study of the minimum Hellinger distance estimator of multivariate, gaussian, stationary, isotropic long-memory random fields The variables are observed on a finite set of points in space. We establish under certain assumptions, the almost sure convergence and the asymptotic distribution of this estimator.

Covariance tapering for multivariate Gaussian random fields estimation

2015 ◽  
Vol 25 (1) ◽  
pp. 21-37 ◽  
Author(s):  
M. Bevilacqua ◽  
A. Fassò ◽  
C. Gaetan ◽  
E. Porcu ◽  
D. Velandia
Keyword(s):  
Random Fields ◽  
Gaussian Random Fields ◽  
Covariance Tapering ◽  
Multivariate Gaussian ◽  
Multivariate Gaussian Random Fields

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.

scholarly journals Extremes of Homogeneous Gaussian Random Fields

2015 ◽  
Vol 52 (1) ◽  
pp. 55-67 ◽  
Author(s):  
Krzysztof Dębicki ◽  
Enkelejd Hashorva ◽  
Natalia Soja-Kukieła
Keyword(s):  
Correlation Function ◽  
Asymptotic Expansion ◽  
Random Fields ◽  
Survival Function ◽  
Random Variable ◽  
Gaussian Random Fields ◽  
Extremal Index ◽  
Gaussian Field ◽  
Gaussian Fields ◽  
Sample Paths

Let {X(s, t): s, t ≥ 0} be a centred homogeneous Gaussian field with almost surely continuous sample paths and correlation function r(s, t) = cov(X(s, t), X(0, 0)) such that r(s, t) = 1 - |s|α1 - |t|α2 + o(|s|α1 + |t|α2), s, t → 0, with α1, α2 ∈ (0, 2], and r(s, t) < 1 for (s, t) ≠ (0, 0). In this contribution we derive an asymptotic expansion (as u → ∞) of P(sup(sn1(u),tn2(u)) ∈[0,x]∙[0,y]X(s, t) ≤ u), where n1(u)n2(u) = u2/α1+2/α2Ψ(u), which holds uniformly for (x, y) ∈ [A, B]2 with A, B two positive constants and Ψ the survival function of an N(0, 1) random variable. We apply our findings to the analysis of extremes of homogeneous Gaussian fields over more complex parameter sets and a ball of random radius. Additionally, we determine the extremal index of the discretised random field determined by X(s, t).

scholarly journals Independence of the increments of Gaussian random fields

1982 ◽  
Vol 85 ◽  
pp. 251-268 ◽  
Author(s):  
Kazuyuki Inoue ◽  
Akio Noda
Keyword(s):  
Random Field ◽  
Random Fields ◽  
Euclidean Distance ◽  
Gaussian Random Field ◽  
Gaussian Random Fields

Let be a mean zero Gaussian random field (n ⋜ 2). We call X Euclidean if the probability law of the increments X(A) − X(B) is invariant under the Euclidean motions. For such an X, the variance of X(A) − X(B) can be expressed in the form r(|A − B|) with a function r(t) on [0, ∞) and the Euclidean distance |A − B|.

scholarly journals Maxima of moving sums in a Poisson random field

2009 ◽  
Vol 41 (03) ◽  
pp. 647-663
Author(s):  
Hock Peng Chan
Keyword(s):  
Random Field ◽  
Random Fields ◽  
Gaussian Random Fields ◽  
Occupation Measure ◽  
Tail Probabilities ◽  
Alternative Representation ◽  
Asymptotic Formulae ◽  
Shape And Size ◽  
Asymptotic Tail

In this paper we examine the extremal tail probabilities of moving sums in a marked Poisson random field. These sums are computed by adding up the weighted occurrences of events lying within a scanning set of fixed shape and size. We also provide an alternative representation of the constants of the asymptotic formulae in terms of the occupation measure of the conditional local random field at zero, and extend these representations to the constants of asymptotic tail probabilities of Gaussian random fields.

Sign in / Sign up

Export Citation Format

Share Document