Vector random fields on the probability simplex with metric-dependent covariance matrix functions. (English) Zbl 1517.60055
Summary: 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.
MSC:
| 60G60 | Random fields |
| 60G22 | Fractional processes, including fractional Brownian motion |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62M20 | Inference from stochastic processes and prediction |
Keywords:
elliptically contoured random field; Gaussian random field; isotropy; ultraspherical polynomialsReferences:
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