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Teor. Veroyatnost. i Primenen., 2016, Volume 61, Issue 3, Pages 547–562 (Mi tvp5072)  

This article is cited in 1 scientific paper (total in 1 paper)

Binomial-$\chi^2$ vector random fields

Ch. Ma

Department of Mathematics and Statiatics, Wichita State University

Abstract: We introduce a new class of non-Gaussian vector random fields in space and/or time, which are termed binomial-$\chi^2$ vector random fields and include $\chi^2$ vector random fields as special cases. We define a binomial-$\chi^2$ vector random field as a binomial sum of squares of independent Gaussian vector random fields on a spatial, temporal, or spatio-temporal index domain. This is a second-order vector random field and has an interesting feature in that its finite-dimensional Laplace transforms are not determined by its own covariance matrix function, but rather by that of the underlying Gaussian one. We study the basic properties of binomial-$\chi^2$ vector random fields and derive some direct/cross covariances, which are based on the bivariate normal density, distribution, and related functions, for elliptically contoured and binomial-$\chi^2$ vector random fields.

Keywords: $\chi^2$ vector random fields, Gaussian vector random fields, elliptically contoured vector random fields, covariance matrix function.

DOI: https://doi.org/10.4213/tvp5072

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English version:
Theory of Probability and its Applications, 2017, 61:3, 375–388

Bibliographic databases:

Received: 17.10.2013
Revised: 06.06.2016
Language:

Citation: Ch. Ma, “Binomial-$\chi^2$ vector random fields”, Teor. Veroyatnost. i Primenen., 61:3 (2016), 547–562; Theory Probab. Appl., 61:3 (2017), 375–388

Citation in format AMSBIB
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  • https://doi.org/10.4213/tvp5072
  • http://mi.mathnet.ru/eng/tvp/v61/i3/p547

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. F. Wang, Ch. Ma, “L(1)-symmetric vector random fields”, Stoch. Process. Their Appl., 129:7 (2019), 2466–2484  crossref  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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