Vector random fields on the probability simplex with metric-dependent covariance matrix functions

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Issue Date
2022-12-01
Authors
Ma, Chunsheng
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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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