$K$-differenced vector random fields
Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 3, pp. 482-499
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A thin-tailed vector random field, referred to as a $K$-differenced vector random field, is introduced.
Its finite-dimensional densities are the differences of two Bessel functions of second order, whenever
they exist, and its finite-dimensional characteristic functions have simple closed forms as the
differences of two power functions or logarithm functions. Its finite-dimensional distributions have thin
tails, even thinner than those of a Gaussian one, and it reduces to a Linnik or Laplace vector random
field in a limiting case. As one of its most valuable properties, a $K$-differenced vector random field is
characterized by its mean and covariance matrix functions just like a Gaussian one. Some covariance
matrix structures are constructed in this paper for not only the $K$-differenced vector random field, but
also for other second-order elliptically contoured vector random fields. Properties of the multivariate
$K$-differenced distribution are also studied.
Keywords:
covariance matrix function, cross covariance, direct covariance, elliptically contoured random field,
Gaussian random field, $K$-differenced distribution, spherically invariant random
field, stationary, variogram.
@article{TVP_2018_63_3_a4,
author = {R. Alsultan and Ch. Ma},
title = {$K$-differenced vector random fields},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {482--499},
publisher = {mathdoc},
volume = {63},
number = {3},
year = {2018},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TVP_2018_63_3_a4/}
}
R. Alsultan; Ch. Ma. $K$-differenced vector random fields. Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 3, pp. 482-499. http://geodesic.mathdoc.fr/item/TVP_2018_63_3_a4/