Vector random fields on the probability simplex with metric-dependent covariance matrix functions
Ma, Chunsheng
Ma, Chunsheng
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2022-12-01
Type
Article
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Keywords
Elliptically contoured random field,Gaussian random field,Isotropy,Ultraspherical polynomials
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Citation
Ma, C. Vector Random Fields on the Probability Simplex with Metric-Dependent Covariance Matrix Functions. J Theor Probab (2022). https://doi.org/10.1007/s10959-022-01217-6
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.
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Publisher
Springer Nature
Journal
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Series
Journal of Theoretical Probability
2022
2022
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ISSN
1572-9230