scholarly journals Efficient Simulation of Stationary Multivariate Gaussian Random Fields with Given Cross-Covariance

2016 ◽  
Vol 07 (17) ◽  
pp. 2183-2194 ◽  
Author(s):  
Jakob Teichmann ◽  
Karl-Gerald van den Boogaart
Keyword(s):  
Random Fields ◽  
Gaussian Random Fields ◽  
Efficient Simulation ◽  
Cross Covariance ◽  
Multivariate Gaussian ◽  
Multivariate Gaussian Random Fields

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

scholarly journals Fast generation of isotropic Gaussian random fields on the sphere

2018 ◽  
Vol 24 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Peter E. Creasey ◽  
Annika Lang
Keyword(s):  
Efficient Method ◽  
Unit Sphere ◽  
Random Fields ◽  
Fourier Transforms ◽  
Gaussian Random Fields ◽  
Covariance Matrices ◽  
Conditional Covariance ◽  
Efficient Simulation ◽  
Set Up ◽  
Markov Properties

Abstract The efficient simulation of isotropic Gaussian random fields on the unit sphere is a task encountered frequently in numerical applications. A fast algorithm based on Markov properties and fast Fourier transforms in 1d is presented that generates samples on an {n\times n} grid in {\operatorname{O}(n^{2}\log n)} . Furthermore, an efficient method to set up the necessary conditional covariance matrices is derived and simulations demonstrate the performance of the algorithm. An open source implementation of the code has been made available at https://github.com/pec27/smerfs.

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