Vector Random Fields on the Probability Simplex with Metric-Dependent Covariance Matrix Functions

Chunsheng Ma ()
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Chunsheng Ma: Wichita State University

Journal of Theoretical Probability, 2023, vol. 36, issue 3, 1922-1938

Abstract: Abstract This paper constructs a class of isotropic vector random fields on the probability simplex via infinite series expansions involving the ultraspherical polynomials, whose covariance matrix functions are functions of the metric (distance function) on the probability simplex, and introduces the scalar and vector fractional, bifractional, and trifractional Brownian motions over the probability simplex, while the metric is shown to be conditionally negative definite.

Keywords: Elliptically contoured random field; Gaussian random field; Isotropy; Ultraspherical polynomials; 60G22; 62M10; 62M20 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-022-01217-6

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