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Teor. Veroyatnost. i Primenen., 2018, Volume 63, Issue 3, Pages 482–499 (Mi tvp5119)  

$K$-differenced vector random fields

R. Alsultan, Ch. Ma

Department of Mathematics, Statistics, and Physics, Wichita State University, Wichita, KS, USA

Abstract: 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.

DOI: https://doi.org/10.4213/tvp5119

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English version:
Theory of Probability and its Applications, 2019, 63:3, 393–407

Bibliographic databases:

Received: 10.01.2017
Revised: 26.05.2017
Accepted:06.03.2018
Language:

Citation: R. Alsultan, Ch. Ma, “$K$-differenced vector random fields”, Teor. Veroyatnost. i Primenen., 63:3 (2018), 482–499; Theory Probab. Appl., 63:3 (2019), 393–407

Citation in format AMSBIB
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\jour Teor. Veroyatnost. i Primenen.
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\pages 482--499
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\crossref{https://doi.org/10.4213/tvp5119}
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\transl
\jour Theory Probab. Appl.
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\pages 393--407
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