scholarly journals Series representations of isotropic vector random fields on balls

2020 ◽  
Vol 156 ◽  
pp. 108583
Author(s):  
Tianshi Lu ◽  
Nikolai Leonenko ◽  
Chunsheng Ma
Keyword(s):  
Random Fields ◽  
Isotropic Vector ◽  
Series Representations

Covariance Matrix Functions of Isotropic Vector Random Fields

2014 ◽  
Vol 43 (10-12) ◽  
pp. 2081-2093 ◽  
Author(s):  
Renxiang Wang ◽  
Juan Du ◽  
Chunsheng Ma
Keyword(s):  
Covariance Matrix ◽  
Random Fields ◽  
Matrix Functions ◽  
Isotropic Vector

scholarly journals Series representations and simulations of isotropic random fields in the Euclidean space

2021 ◽  
Vol 105 (0) ◽  
pp. 93-111
Author(s):  
Z. Ma ◽  
C. Ma
Keyword(s):  
Euclidean Space ◽  
Random Fields ◽  
Spectral Representation ◽  
Series Representation ◽  
Gaussian Random Fields ◽  
Mean Square ◽  
Ultraspherical Polynomial ◽  
Series Representations ◽  
Non Gaussian ◽  
Isotropic Random

This paper introduces the series expansion for homogeneous, isotropic and mean square continuous random fields in the Euclidean space, which involves the Bessel function and the ultraspherical polynomial, but differs from the spectral representation in terms of the ordinary spherical harmonics that has more terms at each level.The series representation provides a simple and efficient approach for simulation of isotropic (non-Gaussian) random fields.

Comparison of Nonlinear Spatial Correlation Models by the Influence of the Data Augmentation to the Classification Risk

2002 ◽  
Vol 7 (1) ◽  
pp. 31-42
Author(s):  
J. Šaltytė ◽  
K. Dučinskas
Keyword(s):  
Spatial Correlation ◽  
Random Fields ◽  
Data Augmentation ◽  
Gaussian Random Fields ◽  
Classification Rule ◽  
Numerical Comparison ◽  
First Order ◽  
Bayesian Risk ◽  
Correlation Models

The Bayesian classification rule used for the classification of the observations of the (second-order) stationary Gaussian random fields with different means and common factorised covariance matrices is investigated. The influence of the observed data augmentation to the Bayesian risk is examined for three different nonlinear widely applicable spatial correlation models. The explicit expression of the Bayesian risk for the classification of augmented data is derived. Numerical comparison of these models by the variability of Bayesian risk in case of the first-order neighbourhood scheme is performed.

Sign in / Sign up

Export Citation Format

Share Document